The work done in a constant pressure expansion can be determined by:

The work done in a constant pressure expansion can be determined by:

A. P(V2 - V1)

B. P(V1 - V2)

C. (P1V1 - P2V2)/r - 1

D. PV x 2.3 log V1/V2

E. P1V1 - P2V2

Answer: A

If 10.4 m³ of air is compressed at a constant temperature to 5.1 m³ and 750 kPa gauge. Calculate how much work is done on the gas, assuming atmospheric pressure to be 100 kPa.

If 10.4 m³ of air is compressed at a constant temperature to 5.1 m³ and 750 kPa gauge. Calculate how much work is done on the gas, assuming atmospheric pressure to be 100 kPa.

A. 2727 J

B. 2850 J

C. 3051 J

D. 3089 J

E. 3128 J

Answer: D

Boyle's Law is one of constant:

Boyle's Law is one of constant:

A. Mass

B. Volume

C. Pressure

D. Temperature

E. Flow


Answer: D

The pressure-volume diagram of a typical air compressor will have a curve drawn:

The pressure-volume diagram of a typical air compressor will have a curve drawn:

A. As an adiabatic compression

B. As in an isothermal compression

C. Approximately half way between the adiabatic and isothermal curves

D. Almost as a straight line

E. From left to right in increasing value curved up


Answer: C

If the volume of a confined gas is constant then the absolute pressure is directly proportional to the absolute temperature according to:

If the volume of a confined gas is constant then the absolute pressure is directly proportional to the absolute temperature according to:

A. Boyle's Law

B. Bernoulli's' Law

C. Charles' Law

D. The General Gas Law

E. Gay-Lussac's Law


Answer: E

Find the characteristic constant for a gas if 112 kg of the gas has a volume of 5.7 m³ at 1500 kPa absolute and 27.5°C.

Find the characteristic constant for a gas if 112 kg of the gas has a volume of 5.7 m³ at 1500 kPa absolute and 27.5°C.

A. 0.254 kJ/kg K

B. 0.261 kJ/kg K

C. 0.271 kJ/kg K

D. 0.274 kJ/kg K

E. 0.291 kJ/kg K

Answer: A

If 24,500 kJ of work is done in a cylinder when 115 kg of a perfect gas is expanded isothermally at 210°C from 0.035 m³ to 6.9 m³. Find the characteristic constant for this gas.

If 24,500 kJ of work is done in a cylinder when 115 kg of a perfect gas is expanded isothermally at 210°C from 0.035 m³ to 6.9 m³. Find the characteristic constant for this gas.

A. 0.083 kJ/kg K

B. 0.198 kJ/kg K

C. 0.421 kJ/kg K

D. 0.441 kJ/kg K

E. 0.489 kJ/kg K


Answer: A

A gas at 1000 kPa gauge pressure and 30°C is transferred from a cylindrical vessel 1.5 m in diameter and 3 m long to another cylindrical vessel 2.5 m in diameter and 5 m long. If the new gauge pressure is 150 kPa, calculate the new temperature. Note: Assume atmospheric pressure to be 100 kPa for this calculation.

A gas at 1000 kPa gauge pressure and 30°C is transferred from a cylindrical vessel 1.5 m in diameter and 3 m long to another cylindrical vessel 2.5 m in diameter and 5 m long. If the new gauge pressure is 150 kPa, calculate the new temperature. Note: Assume atmospheric pressure to be 100 kPa for this calculation.

A. 350°C

B. 318°C

C. 45.9°C

D. 63.7°C

E. 436°C


Answer: C

If 0.25 m³ of a gas at 4000 kPa gauge pressure is expanded until the gauge pressure is 500 kPa and the expansion is polytropic with n = 1.35. Find the final volume the gas will occupy. Note: Assume atmospheric pressure = 100 kPa

If 0.25 m³ of a gas at 4000 kPa gauge pressure is expanded until the gauge pressure is 500 kPa and the expansion is polytropic with n = 1.35. Find the final volume the gas will occupy. Note: Assume atmospheric pressure = 100 kPa

A. 1.04 m³

B. 1.24 m³

C. 1.30 m³

D. 1.33 m³

E. 1.47 m³


Answer: A

The equation (PV/T) = mR or PV = mRT is called the:

The equation (PV/T) = mR or PV = mRT is called the:

A. Characteristic equation of a perfect gas

B. Characteristic constant of a perfect gas

C. Perfect gas law equation

D. Volume constant for perfect gases

E. Boyle's law


Answer: A

The Characteristic Constant of each perfect gas is

The Characteristic Constant of each perfect gas is

A. The same for all perfect gases

B. The same for all gases if their temperatures are the same

C. The same for all gases if their pressures are the same

D. Unique to that particular gas

E. Varying directly with temperature changes


Answer: D

The pressure-volume diagram of a typical air compressor will have a curve drawn:

The pressure-volume diagram of a typical air compressor will have a curve drawn:

A. As an adiabatic compression

B. As in an isothermal compression

C. Approximately half way between the adiabatic and isothermal curves

D. Almost as a straight line

E. From left to right in increasing value curved up

Answer: C

If 10.4 m³ of air is compressed at a constant temperature to 5.1 m³ and 750 kPa gauge. Calculate how much work is done on the gas, assuming atmospheric pressure to be 100 kPa.

If 10.4 m³ of air is compressed at a constant temperature to 5.1 m³ and 750 kPa gauge. Calculate how much work is done on the gas, assuming atmospheric pressure to be 100 kPa.

A. 2727 J

B. 2850 J

C. 3051 J

D. 3089 J

E. 3128 J


Answer: D

Compression and expansion in real life cases will always follow the polytropic process that is described by the formula(s):

Compression and expansion in real life cases will always follow the polytropic process that is described by the formula(s): 

1. P1V1 = P2V2
2. P1V1n = P2V2n
3. PVn = Constant
4. PV = Constant


A. 1, 2

B. 2, 3

C. 3, 4

D. 1, 3

E. 2, 4


Answer: B

The formula Work = (P1V1 - P2V2) / n - 1 is used to describe expansion during:

The formula Work = (P1V1 - P2V2) / n - 1 is used to describe expansion during:

A. An isothermal process

B. An isentropic process

C. A polytropic process

D. An adiabatic process

E. An enthalpy process


Answer: C

To "expand a gas" means the gas is:

To "expand a gas" means the gas is:

A. Always at constant volume

B. Always at constant pressure

C. Always at constant temperature

D. Able to perform useful work

E. Required to have work preformed on it


Answer: D

The work done in a constant pressure expansion can be determined by:

The work done in a constant pressure expansion can be determined by:

A. P(V2 - V1)

B. P(V1 - V2)

C. (P1V1 - P2V2)/r - 1

D. PV x 2.3 log V1/V2

E. P1V1 - P2V2


Answer: A

A perfect gas is compressed under conditions of constant temperature to a volume of 30 m³. If the final pressure of the gas is 450 kPa gauge and the initial volume was 135 m³, what was the initial pressure? (Assume atmospheric pressure to be 101.3 kPa)

A perfect gas is compressed under conditions of constant temperature to a volume of 30 m³. If the final pressure of the gas is 450 kPa gauge and the initial volume was 135 m³, what was the initial pressure? (Assume atmospheric pressure to be 101.3 kPa)

A. 122.5 kPa gauge

B. 21.2 kPa gauge

C. 223.8 kPa gauge

D. 101.3 kPa gauge

E. 124.8 kPa gauge


Answer: B

Gases such as air, nitrogen and oxygen can be roughly defined as perfect gases because they:

Gases such as air, nitrogen and oxygen can be roughly defined as perfect gases because they:

A. Condense rapidly during condition changes

B. Can expand without being heated

C. Remain in gaseous form during condition changes

D. Cannot be superheated

E. None of the above


Answer: C

The General Gas Law can be written using the formula/s:

The General Gas Law can be written using the formula/s: 

1. PV/T = C (constant)
2. P1V1/T2 = P2V2/T1
3. P1V1/T1 = P2V2/T2
4. P1V2/T1 = P2V1/T2


A. 1, 2

B. 2, 3

C. 3, 4

D. 1, 3

E. 2, 4


Answer: D

The pressure-volume diagram of a typical air compressor will have a curve drawn:

The pressure-volume diagram of a typical air compressor will have a curve drawn:

A. As an adiabatic compression

B. As in an isothermal compression

C. Approximately half way between the adiabatic and isothermal curves

D. Almost as a straight line

E. From left to right in increasing value curved up


Answer: C

Absolute pressure can be defined as:

Absolute pressure can be defined as:

A. The pressure at which a perfect gas will turn to a liquid

B. The sum of the gauge pressure reading plus atmospheric pressure

C. The difference between the gauge pressure minus the atmospheric pressure

D. A pressure constant used in the calculation of pressure volume equations

E. The highest pressure that a substance can endure


Answer: B

How much work is required to compress a gas polytropically from 195 kPa abs to 1600 kPa abs while reducing the volume to 0.8 m3? Use the value of "n" for this gas as 1.35.

How much work is required to compress a gas polytropically from 195 kPa abs to 1600 kPa abs while reducing the volume to 0.8 m3? Use the value of "n" for this gas as 1.35.

A. 399.26 kJ

B. 758.95 kJ

C. 1540 kJ

D. 1735 kJ

E. 1889 kJ


Answer: C

If 1.45 m³ of air at 100 kPa abs and 12°C is compressed to 950 kPa abs while following the law PV1.34 = C. Taking R for air = 0.287 kJ/kg K, find the final volume of air and the mass of air compressed.

If 1.45 m³ of air at 100 kPa abs and 12°C is compressed to 950 kPa abs while following the law PV1.34 = C. Taking R for air = 0.287 kJ/kg K, find the final volume of air and the mass of air compressed.

A. V2 = 0.27 m³ and mass = 1.77 kg

B. V2 = 0.42 m³ and mass = 3.55 kg

C. V2 = 0.27 m³ and mass = 42.1 kg

D. V2 = 0.42 m³ and mass = 57.5 kg

E. V2 = 0.42 m³ and mass = 42.1 kg



Answer: A

The characteristic constant for a gas is given as:

The characteristic constant for a gas is given as:

A. Kg/kPa/K

B. J/g C

C. KJ/Kg/C

D. Kg K

E. KJ/Kg K


Answer: E

Steam that is superheated:

Steam that is superheated:

A. Has a greater specific volume than saturated steam at the same pressure

B. Has less heat than saturated steam at the same pressure

C. Contains more energy but has the same temperature as saturated steam

D. Has a volume equal to that of saturated steam

E. All of the above


Answer: A

Steam with a percentage of wetness is said to have insufficient:

Steam with a percentage of wetness is said to have insufficient:

A. Temperature

B. Sensible heat

C. Total enthalpy

D. Internal energy

E. Latent heat


Answer: E

The total amount of heat, in kJ, that is absorbed by the water/steam in a boiler in a given period of time is called the:

The total amount of heat, in kJ, that is absorbed by the water/steam in a boiler in a given period of time is called the:

A. Heat rate

B. Factor of evaporation

C. Equivalent evaporation

D. Total enthalpy

E. Latent heat of the transformation


Answer: A

The ratio of the heat energy required to make steam to the heat energy supplied by the combustion of fuel in a boiler is called:

The ratio of the heat energy required to make steam to the heat energy supplied by the combustion of fuel in a boiler is called:

A. Boiler efficiency

B. Factor of evaporation

C. Heat rate

D. Combustion efficiency

E. Equivalent evaporation


Answer: A

Referring to the diagram below, the point marked as 2 represents:

Referring to the diagram below, the point marked as 2 represents:

A. Superheated steam

B. Wet steam

C. Dry saturated steam

D. Boiling water

E. Critical point


Answer: D

Critical pressure, critical temperature and critical volume are the terms given to those points in the state of a substance at which:

Critical pressure, critical temperature and critical volume are the terms given to those points in the state of a substance at which:

A. Liquid and vapor have identical properties

B. Liquid and vapor have different properties

C. The critical temperature and pressure are the same

D. Vapor properties are exactly double liquid properties

E. Critical pressure and critical volume are the same


Answer: A

What is the enthalpy of 75% dry steam at 1300 kPa?

What is the enthalpy of 75% dry steam at 1300 kPa?

A. 1720.84 kJ

B. 2090.7 kJ

C. 2787.6 kJ

D. 2294.45 kJ

E. 1972.7 kJ


Answer: D

Superheated steam is steam at a certain pressure, which temperature is above the:

Superheated steam is steam at a certain pressure, which temperature is above the:

A. Combustion gas temperature

B. Radiant steam temperature

C. Fusion temperature

D. Saturation temperature

E. Critical temperature


Answer: D

How many degrees of superheat are there in steam at 4000 kPa and 900°C?

How many degrees of superheat are there in steam at 4000 kPa and 900°C?

A. 649.6°C

B. 250.4°C

C. 900°C

D. 263.99°C

E. 445.8°C


Answer: A

If a boiler has a factor of evaporation of 1.075 and its actual flow rate is 220 kg/min, calculate the equivalent evaporation in kg/hr.

If a boiler has a factor of evaporation of 1.075 and its actual flow rate is 220 kg/min, calculate the equivalent evaporation in kg/hr.

A. 32871 kg/hr

B. 13200 kg/hr

C. 12279 kg/hr

D. 236.5 kg/hr

E. 14190 kg/hr


Answer: E

If the enthalpy of each kg of steam is only 2650.3 kJ and the pressure is 4000 kPa, calculate the dryness fraction.

If the enthalpy of each kg of steam is only 2650.3 kJ and the pressure is 4000 kPa, calculate the dryness fraction.

A. 95%

B. 75%

C. 91%

D. 89%

E. 82%


Answer: C

Referring to the diagram below, the point marked as 3 represents

Referring to the diagram below, the point marked as 3 represents

A. Superheated steam

B. Wet saturated steam

C. Dry saturated steam

D. Boiling water

E. Critical point


Answer: C

The mass of water that would be evaporated in one hour, from feedwater at 100°C into dry saturated steam at 100°C, by the same amount of heat that is required, per hour, to produce steam at the actual boiler condition is called the:

The mass of water that would be evaporated in one hour, from feedwater at 100°C into dry saturated steam at 100°C, by the same amount of heat that is required, per hour, to produce steam at the actual boiler condition is called the:

A. Heat rate

B. Factor of evaporation

C. Equivalent evaporation

D. Total enthalpy

E. Latent heat of the transformation


Answer: C

The amount of heat required to convert 10 kg of water at 60°C into dry saturated steam at 200 kPa is:

The amount of heat required to convert 10 kg of water at 60°C into dry saturated steam at 200 kPa is:

A. 2455.57 kJ

B. 2511.3 kJ

C. 2706.7 kJ

D. 24,555.7 kJ

E. 27,067 kJ


Answer: D

Dry saturated steam is steam saturated with ________________.

Dry saturated steam is steam saturated with ________________.

A. Water

B. All its latent heat

C. A percentage of "hfg"

D. Sensible heat

E. A percentage of "hf"


Answer: B

A boiler generates 10 kg of dry steam per 2 kg of coal burned. The heating value of the coal is 21,000 kJ/kg. The boiler produces 1500 kPa steam from 60°C feedwater. Calculate the efficiency.

A boiler generates 10 kg of dry steam per 2 kg of coal burned. The heating value of the coal is 21,000 kJ/kg. The boiler produces 1500 kPa steam from 60°C feedwater. Calculate the efficiency.

A. 57.3%

B. 92.3%

C. 60.5%

D. 74.7%

E. 85.0%


Answer: C

On the temperature-enthalpy diagram for steam, the point corresponding to a temperature of 374.12°C and pressure of 22,090 kPa is called the:

On the temperature-enthalpy diagram for steam, the point corresponding to a temperature of 374.12°C and pressure of 22,090 kPa is called the:

A. Critical point

B. Boiling point

C. Superheat pressure and temperature

D. Steam-water saturation point

E. Point of absolute temperature and pressure


Answer: A

The dryness fraction, also called steam quality, is the percentage:

The dryness fraction, also called steam quality, is the percentage:

A. By mass of steam in the mixture

B. By volume of water to steam of the mixture

C. By volume of steam in the mixture

D. Of water by weight in the steam

E. By weight of steam and water in the mixture


Answer: A

How many kJ of heat is required to produce 32 kg of steam 88% dry at 3000 kPa from feedwater at 90°C?

How many kJ of heat is required to produce 32 kg of steam 88% dry at 3000 kPa from feedwater at 90°C?

A. 70774.9 kJ

B. 64210.6 kJ

C. 2211.7 kJ

D. 10994.2 kJ

E. 2804.2 kJ


Answer: A

What is the enthalpy of 75% dry steam at 1300 kPa?

What is the enthalpy of 75% dry steam at 1300 kPa?

A. 1720.84 kJ

B. 2090.7 kJ

C. 2787.6 kJ

D. 2294.45 kJ

E. 1972.7 kJ


Answer: D

Five kilograms of water at 100°C is changed to saturated steam having a final temperature of 120°C. Calculate the total amount of heat required in changing the water to steam.

Five kilograms of water at 100°C is changed to saturated steam having a final temperature of 120°C. Calculate the total amount of heat required in changing the water to steam.

A. 2287.26 kJ

B. 2706.3 kJ

C. 11,436 kJ

D. 13,531.5 kJ

E. 17,138 kJ


Answer: C

A boiler generates 10 kg of dry steam per 2 kg of coal burned. The heating value of the coal is 21,000 kJ/kg. The boiler produces 1500 kPa steam from 60°C feedwater. Calculate the efficiency.

A boiler generates 10 kg of dry steam per 2 kg of coal burned. The heating value of the coal is 21,000 kJ/kg. The boiler produces 1500 kPa steam from 60°C feedwater. Calculate the efficiency.

A. 57.3%

B. 92.3%

C. 60.5%

D. 74.7%

E. 85.0%


Answer: C

Superheated steam is steam at a certain pressure, which temperature is above the:

Superheated steam is steam at a certain pressure, which temperature is above the:

A. Combustion gas temperature

B. Radiant steam temperature

C. Fusion temperature

D. Saturation temperature

E. Critical temperature


Answer: D

The ratio of the heat energy required to make steam to the heat energy supplied by the combustion of fuel in a boiler is called:

The ratio of the heat energy required to make steam to the heat energy supplied by the combustion of fuel in a boiler is called:

A. Boiler efficiency

B. Factor of evaporation

C. Heat rate

D. Combustion efficiency

E. Equivalent evaporation


Answer: A

The mass of water that would be evaporated in one hour, from feedwater at 100°C into dry saturated steam at 100°C, by the same amount of heat that is required, per hour, to produce steam at the actual boiler condition is called the:

The mass of water that would be evaporated in one hour, from feedwater at 100°C into dry saturated steam at 100°C, by the same amount of heat that is required, per hour, to produce steam at the actual boiler condition is called the:

A. Heat rate

B. Factor of evaporation

C. Equivalent evaporation

D. Total enthalpy

E. Latent heat of the transformation


Answer: C

Steam that is superheated:

Steam that is superheated:

A. Has a greater specific volume than saturated steam at the same pressure

B. Has less heat than saturated steam at the same pressure

C. Contains more energy but has the same temperature as saturated steam

D. Has a volume equal to that of saturated steam

E. All of the above


Answer: A

Determine the total latent heat required to produce 2.3 kg of dry, saturated steam at a pressure of 350 kPa absolute.

Determine the total latent heat required to produce 2.3 kg of dry, saturated steam at a pressure of 350 kPa absolute.

A. 6284.5 kJ

B. 4940.6 kJ

C. 2148.1 kJ

D. 1649.9 kJ

E. 1343.9 kJ


Answer: B

Referring to the diagram below, the point marked as 2 represents:

Referring to the diagram below, the point marked as 2 represents:

A. Superheated steam

B. Wet steam

C. Dry saturated steam

D. Boiling water

E. Critical point


Answer: D

Steam at the temperature of evaporation corresponding to the pressure is, by definition:

Steam at the temperature of evaporation corresponding to the pressure is, by definition:

A. Wet steam

B. Superheated steam

C. Dry steam

D. Sub-cooled steam

E. Saturated steam


Answer: E

How many degrees of superheat are there in steam at 4000 kPa and 900°C?

How many degrees of superheat are there in steam at 4000 kPa and 900°C?

A. 649.6°C

B. 250.4°C

C. 900°C

D. 263.99°C

E. 445.8°C


Answer: A

Heat transfer directly from a flame in a furnace to the furnace waterfalls is an example of:

Heat transfer directly from a flame in a furnace to the furnace waterfalls is an example of:

A. Convection

B. Radiation

C. Conduction

D. Sublimation

E. Condensation


Answer: B

The change in length per unit length per degree rise in temperature is known as the:

The change in length per unit length per degree rise in temperature is known as the:

A. Specific heat

B. Coefficient of linear expansion

C. Coefficient of conductivity

D. Latent heat of fusion

E. Latent heat of evaporation


Answer: B

A 110 m long mild steel pipe in a refinery conveys oil at a maximum temperature of 140°C. In winter the plant is shut down, and the temperature of the pipeline drops to -25°C. Calculate the amount of shrinkage of the pipe.

A 110 m long mild steel pipe in a refinery conveys oil at a maximum temperature of 140°C. In winter the plant is shut down, and the temperature of the pipeline drops to -25°C. Calculate the amount of shrinkage of the pipe.

A. 0.151 8 cm

B. 0.217 8 cm

C. 15.18 cm

D. 21.78 cm

E. 65.34 cm


Answer: D

Heat transfer by electromagnetic waves is called:

Heat transfer by electromagnetic waves is called:

A. Radiation

B. Conduction

C. Convection

D. Emission

E. Electromagnetic transmission


Answer: A

If a bar is heated at one end heat will travel from molecule to molecule until the other end becomes hot. This is known as:

If a bar is heated at one end heat will travel from molecule to molecule until the other end becomes hot. This is known as:

A. Convection

B. Radiation

C. Conduction

D. Specific heat

E. Sublimation


Answer: C

If four plates of identical physical dimensions are subjected to the same temperature difference, the one made of which material will conduct the most heat?

If four plates of identical physical dimensions are subjected to the same temperature difference, the one made of which material will conduct the most heat?

A. Aluminum

B. Brass

C. Copper

D. Glass

E. Steel


Answer: C

The transfer of heat by convection involves the:

The transfer of heat by convection involves the:

A. Reduction of mass

B. Movement of a fluid

C. Transfer of elements

D. Radiation of light

E. Contact between molecules


Answer: B

The change in length per unit length per degree rise in temperature is known as the:

The change in length per unit length per degree rise in temperature is known as the:

A. Specific heat

B. Coefficient of linear expansion

C. Coefficient of conductivity

D. Latent heat of fusion

E. Latent heat of evaporation


Answer: B

A copper rod of the same dimensions as a steel rod will:

A copper rod of the same dimensions as a steel rod will:

A. Expand more for a given temperature change

B. Expand less for a given temperature change

C. Heat up slower for a given amount of heat

D. Have the same mass

E. Expand the same at all temperatures


Answer: A

Expansion will result in an increase in a body's surface as well as its:

Expansion will result in an increase in a body's surface as well as its:

A. Temperature

B. Coefficient

C. Volume

D. Pressure

E. Location


Answer: C

If a mild steel cube of side 40 mm is heated from 25°C to 50°C, the increase in volume will be:

If a mild steel cube of side 40 mm is heated from 25°C to 50°C, the increase in volume will be:

A. 5.76 mm³

B. 19.2 mm³

C. 57.6 mm³

D. 192 mm³

E. 64,000 mm³


Answer: C

Heat will always flow between two bodies in contact with each other if they are:

Heat will always flow between two bodies in contact with each other if they are:

A. At different temperatures

B. Different colors

C. Close to each other

D. In a solid state only

E. Made of the same material


Answer: A

Heat transfer by electromagnetic waves is called:

Heat transfer by electromagnetic waves is called:

A. Radiation

B. Conduction

C. Convection

D. Emission

E. Electromagnetic transmission


Answer: A

Radiant energy waves are:

Radiant energy waves are:

A. Able to pass through a vacuum

B. Those that travel in straight lines

C. Absorbed, reflected or transmitted by other bodies

D. Absorbed and converted into heat

E. All of the above


Answer: E

A 110 m long mild steel pipe in a refinery conveys oil at a maximum temperature of 140°C. In winter the plant is shut down, and the temperature of the pipeline drops to -25°C. Calculate the amount of shrinkage of the pipe.

A 110 m long mild steel pipe in a refinery conveys oil at a maximum temperature of 140°C. In winter the plant is shut down, and the temperature of the pipeline drops to -25°C. Calculate the amount of shrinkage of the pipe.

A. 0.151 8 cm

B. 0.217 8 cm

C. 15.18 cm

D. 21.78 cm

E. 65.34 cm


Answer: D

The transfer of heat by convection involves the:

The transfer of heat by convection involves the:

A. Reduction of mass

B. Movement of a fluid

C. Transfer of elements

D. Radiation of light

E. Contact between molecules


Answer: B

Which of the following has the lowest thermal conductivity?

Which of the following has the lowest thermal conductivity?

A. Aluminum

B. Brass

C. Copper

D. Air

E. Steel


Answer: D

A 110 m long mild steel pipe in a refinery conveys oil at a maximum temperature of 140°C. In winter the plant is shut down, and the temperature of the pipeline drops to -25°C. Calculate the amount of shrinkage of the pipe.

A 110 m long mild steel pipe in a refinery conveys oil at a maximum temperature of 140°C. In winter the plant is shut down, and the temperature of the pipeline drops to -25°C. Calculate the amount of shrinkage of the pipe.

A. 0.151 8 cm

B. 0.217 8 cm

C. 15.18 cm

D. 21.78 cm

E. 65.34 cm


Answer: D

Heat transfer directly from a flame in a furnace to the furnace waterfalls is an example of:

Heat transfer directly from a flame in a furnace to the furnace waterfalls is an example of:

A. Convection

B. Radiation

C. Conduction

D. Sublimation

E. Condensation


Answer: B

Transfer of heat by convection depends upon:

Transfer of heat by convection depends upon:

A. The molecular structure of the fluid

B. A dense fluid being displaced by a less dense fluid

C. The color and the texture of the surface of the fluid

D. The viscosity of the fluid

E. A less dense fluid being displaced by a denser fluid


Answer: E

The illustration below is intended to explain the symbols in this mode of heat transfer:

The illustration below is intended to explain the symbols in this mode of heat transfer:

A. Conduction

B. Radiation

C. Convection

D. Specific heat

E. Sublimation


Answer: A

The coefficient of volumetric expansion for solids is:

The coefficient of volumetric expansion for solids is:

A. The cube of the coefficient of linear expansion

B. Three times the coefficient of linear expansion

C. Two times the coefficient of linear expansion

D. The inverse of the coefficient of linear expansion

E. The square root of the coefficient of linear expansion

Answer: B

Heat will always flow between two bodies in contact with each other if they are:

Heat will always flow between two bodies in contact with each other if they are:

A. At different temperatures

B. Different colors

C. Close to each other

D. In a solid state only

E. Made of the same material


Answer: A

Heat transfer by electromagnetic waves is called:

Heat transfer by electromagnetic waves is called:

A. Radiation

B. Conduction

C. Convection

D. Emission

E. Electromagnetic transmission


Answer: A

Calculate the amount of heat required to raise the temperature of 0.5 kg of aluminum by 35°C.

Calculate the amount of heat required to raise the temperature of 0.5 kg of aluminum by 35°C.

A. 2.27 kJ

B. 15.91 kJ

C. 16.5 kJ

D. 22.7 kJ

E. 45.6 kJ

Answer: B

Absolute zero is the temperature at which:

Absolute zero is the temperature at which:

A. Molecular motion ceases

B. Water starts to turn into ice

C. Atmospheric pressure equals zero

D. Heat transfer becomes impossible

E. Energy conversion ceases


Answer: A

Temperature is defined as the:

Temperature is defined as the:

A. Sum of kinetic and potential energy of the molecules which make up the substance

B. Measure of the level of internal energy

C. Amount of energy transferred from one body to another

D. Measure of amount of "caloric" passing from one body to another

E. Measure of kinetic energy of the molecules of a substance


Answer: B

If melted, most substances:

If melted, most substances:

A. Increase their volume

B. Decrease their volume

C. Retain their volume

D. Increase, decrease or retain their volume, depending on conditions

E. Decrease in temperature


Answer: A

82 degrees on the Fahrenheit scale is equal to _____ K on the Kelvin scale:

82 degrees on the Fahrenheit scale is equal to _____ K on the Kelvin scale:

A. 290.7

B. 300.5

C. 310.7

D. 320.5

E. 373.5


Answer: B

The water equivalent of a 0.7 kg brass calorimeter is:

The water equivalent of a 0.7 kg brass calorimeter is:

A. 0.088 kg

B. 0.13 kg

C. 0.064 kg

D. 0.035 kg

E. 0.65 kg


Answer: C

The boiling point on the Rankine scale is:

The boiling point on the Rankine scale is:

A. 100 R

B. 212 R

C. 373 R

D. 460 R

E. 672 R


Answer: E

The absolute temperature equivalent of 30°C is:

The absolute temperature equivalent of 30°C is:

A. -30 K

B. 86°F

C. 86°R

D. 303 K

E. 672°R


Answer: D

65 kg of water at 26°C is poured into 15 kg of ice at -6°C. The resulting temperature of the mixture is:

65 kg of water at 26°C is poured into 15 kg of ice at -6°C. The resulting temperature of the mixture is:

A. 21.4°C

B. 10.91°C

C. 5.53°C

D. 15.7°C

E. 3.65°C


Answer: C

The boiling point of water on the Kelvin scale is:

The boiling point of water on the Kelvin scale is:

A. 100

B. 212

C. 373

D. 460

E. 672


Answer: C

The boiling point on the Rankine scale is:

The boiling point on the Rankine scale is:

A. 100 R

B. 212 R

C. 373 R

D. 460 R

E. 672 R


Answer: E

Calculate the amount of heat required to raise the temperature of 0.5 kg of aluminum by 35°C.

Calculate the amount of heat required to raise the temperature of 0.5 kg of aluminum by 35°C.

A. 2.27 kJ

B. 15.91 kJ

C. 16.5 kJ

D. 22.7 kJ

E. 45.6 kJ


Answer: B

150°F is equivalent to:

150°F is equivalent to:

A. 51.3°C

B. 65.6°C

C. 101.1°C

D. 212.4°C

E. 302°C


Answer: B

82 degrees on the Fahrenheit scale is equal to _____ K on the Kelvin scale:

82 degrees on the Fahrenheit scale is equal to _____ K on the Kelvin scale:

A. 290.7

B. 300.5

C. 310.7

D. 320.5

E. 373.5


Answer: B

The boiling point of water on the Kelvin scale is:

The boiling point of water on the Kelvin scale is:

A. 100

B. 212

C. 373

D. 460

E. 672

Answer: C

72 degrees on the Celsius scale is equal to _____ degrees on the Fahrenheit scale:

72 degrees on the Celsius scale is equal to _____ degrees on the Fahrenheit scale:

A. 156.2

B. 161.6

C. 169.6

D. 173.4

E. 185.2


Answer: B

The water equivalent of a 0.7 kg brass calorimeter is:

The water equivalent of a 0.7 kg brass calorimeter is:

A. 0.088 kg

B. 0.13 kg

C. 0.064 kg

D. 0.035 kg

E. 0.65 kg

Answer: C

A piece of copper absorbs 50 kJ of heat while its temperature rises from 20°C to 70°C. Calculate the mass of the copper.

A piece of copper absorbs 50 kJ of heat while its temperature rises from 20°C to 70°C. Calculate the mass of the copper.

A. 0.333 kg

B. 1.54 kg

C. 2.58 kg

D. 3.50 kg

E. 116 kg


Answer: C

If melted, most substances:

If melted, most substances:

A. Increase their volume

B. Decrease their volume

C. Retain their volume

D. Increase, decrease or retain their volume, depending on conditions

E. Decrease in temperature


Answer: A

Absolute zero is the temperature at which:

Absolute zero is the temperature at which:

A. Molecular motion ceases

B. Water starts to turn into ice

C. Atmospheric pressure equals zero

D. Heat transfer becomes impossible

E. Energy conversion ceases


Answer: A

150°F is equivalent to:

150°F is equivalent to:

A. 51.3°C

B. 65.6°C

C. 101.1°C

D. 212.4°C

E. 302°C


Answer: B

Absolute zero is the temperature at which:

Absolute zero is the temperature at which:

A. Molecular motion ceases

B. Water starts to turn into ice

C. Atmospheric pressure equals zero

D. Heat transfer becomes impossible

E. Energy conversion ceases


Answer: A

The boiling point of water on the Kelvin scale is:

The boiling point of water on the Kelvin scale is:

A. 100

B. 212

C. 373

D. 460

E. 672


Answer: C

Kelvin is the scientific or _____ scale.

Kelvin is the scientific or _____ scale.

A. Perfect

B. Fixed

C. Absolute

D. Correct

E. Proper


Answer: C

90 degrees on the Celsius scale is equal to _____ R on the Rankine scale:

90 degrees on the Celsius scale is equal to _____ R on the Rankine scale:

A. 550

B. 590

C. 630

D. 654

E. 692


Answer: D

Correct term for any change of phase from a liquid to a vapor is:

Correct term for any change of phase from a liquid to a vapor is:

A. Boiling

B. Evaporation

C. Boiling point

D. Vaporization

E. Fusion


Answer: B

The water equivalent of a 0.7 kg brass calorimeter is:

The water equivalent of a 0.7 kg brass calorimeter is:

A. 0.088 kg

B. 0.13 kg

C. 0.064 kg

D. 0.035 kg

E. 0.65 kg


Answer: C

In the SI system the temperature scales used are:

In the SI system the temperature scales used are:

A. Celsius and Kelvin

B. Fahrenheit and Rankine

C. Absolute and Adiabatic

D. Endothermic and Isothermic

E. Kelvin and Rankine


Answer: A

Heat is a form of energy and when applied to a body it:

Heat is a form of energy and when applied to a body it:

A. Decreases the temperature

B. Increases the energy of that body

C. Increases the latent heat

D. Decreases the sensible heat

E. Decreases the internal energy of that body


Answer: B

Calculate the amount of heat required to raise the temperature of 0.5 kg of aluminum by 35°C.

Calculate the amount of heat required to raise the temperature of 0.5 kg of aluminum by 35°C.

A. 2.27 kJ

B. 15.91 kJ

C. 16.5 kJ

D. 22.7 kJ

E. 45.6 kJ


Answer: B

A block of wood measures 20 cm wide x 15 cm deep and has a specific gravity of 0.75. If its mass is 8 kg, find the length of the block.

A block of wood measures 20 cm wide x 15 cm deep and has a specific gravity of 0.75. If its mass is 8 kg, find the length of the block.

A. 3.56 cm

B. 13.56 cm

C. 35.6 cm

D. 105 mm

E. 10,667 cm

Answer: C

A solid cylinder is 31 cm in diameter by 2.4 m long. It has the same mass as a lead cube with 0.5 m sides. What material is the cylinder likely made of?

A solid cylinder is 31 cm in diameter by 2.4 m long. It has the same mass as a lead cube with 0.5 m sides. What material is the cylinder likely made of?

A. Mild steel

B. Tin

C. Brass

D. Copper

E. Cobalt


Answer: A

In a fluid contained by solid boundaries the pressure exerted by the enclosed fluid on its boundaries is always:

In a fluid contained by solid boundaries the pressure exerted by the enclosed fluid on its boundaries is always:

A. Normal or prependicular

B. Constant in all directions

C. Equal

D. Measured in kgs

E. Acting on the side and bottoms


Answer: A

The wheel-and-axle system below has dimensions d = 300 mm and R = 1.5 m. If the efficiency of the machine is 90%, find the mechanical advantage of the system.

The wheel-and-axle system below has dimensions d = 300 mm and R = 1.5 m. If the efficiency of the machine is 90%, find the mechanical advantage of the system.

A. 4.5

B. 5

C. 7

D. 9

E. 10


Answer: D

A bar with a diameter of 494 mm and a length of 1.5 m has a square hole with 177.8 mm sides through its axis. If the mass of the bar is 2027.1 kg, find the relative density of this material.

A bar with a diameter of 494 mm and a length of 1.5 m has a square hole with 177.8 mm sides through its axis. If the mass of the bar is 2027.1 kg, find the relative density of this material.

A. 10.7

B. 9.77

C. 9.77 kg/m³

D. 8.44

E. 8.44 kg/m³


Answer: D

Specific Gravity used in the Imperial system is equivalent to the _____ used in the metric system.

Specific Gravity used in the Imperial system is equivalent to the _____ used in the metric system.

A. Relative density

B. Relative gravity

C. Specific density

D. Weight density

E. Specific weight


Answer: A

A pile of coal that forms a perfect cone shape has a base area of 24 m² and a height of 15 m. Assuming the pile has 25 percent of void space, and that the density of the coal given is 1400 kg/m³, determine the mass of the coal in this pile.

A pile of coal that forms a perfect cone shape has a base area of 24 m² and a height of 15 m. Assuming the pile has 25 percent of void space, and that the density of the coal given is 1400 kg/m³, determine the mass of the coal in this pile.

A. 12,600 kg

B. 14,700 kg

C. 54,000 kg

D. 126 t

E. 168 t


Answer: D

"Standard conditions" used to compare mass densities of several substance are set at _____ atmosphere pressure.

"Standard conditions" used to compare mass densities of several substance are set at _____ atmosphere pressure.

A. 25°C and 25

B. 20°C and 1

C. 20°C and 0

D. 0°C and 0

E. 0°C and 1


Answer: E

An oil well is 2 kilometers in depth. What pressure is necessary at the bottom of the well in order to force oil of relative density 0.70 to the top.

An oil well is 2 kilometers in depth. What pressure is necessary at the bottom of the well in order to force oil of relative density 0.70 to the top.

A. 14,000 Pa

B. 536.76 kPa

C. 686.7 kPa

D. 1400 kPa

E. 13,734 KPa

Answer: E

A steel storage tank is 5 m long, 2 m wide and 4 m high. It is 60% full of ethylene glycol with a relative density of 1.1. What is the force load exerted by the fluid on one end?

A steel storage tank is 5 m long, 2 m wide and 4 m high. It is 60% full of ethylene glycol with a relative density of 1.1. What is the force load exerted by the fluid on one end?

A. 51.9 kN

B. 42.5 kN

C. 172.8 kN

D. 62.2 kN

E. 103.6 kN


Answer: D

A cylindrical tank has its axis vertical. It is 2 m in diameter and its mass is 800 kg. When it is filled to 2 m high with oil, the total mass is 5050 kg. What is the relative density of the oil?

A cylindrical tank has its axis vertical. It is 2 m in diameter and its mass is 800 kg. When it is filled to 2 m high with oil, the total mass is 5050 kg. What is the relative density of the oil?

A. 6.312

B. 6.764 kg/m³

C. 6.764

D. 0.876

E. 0.6764


Answer: E

A pipe has an inside diameter of 4 cm with a water flow of 5,000 L/hr. What is the velocity of the water?

A pipe has an inside diameter of 4 cm with a water flow of 5,000 L/hr. What is the velocity of the water?

A. 1.1 m/s

B. 2.2 m/s

C. 3.3 m/s

D. 4.4 m/s

E. 5.5 m/s

Answer: A

A bar with a diameter of 494 mm and a length of 1.5 m has a square hole with 177.8 mm sides through its axis. If the mass of the bar is 2027.1 kg, find the relative density of this material.

A bar with a diameter of 494 mm and a length of 1.5 m has a square hole with 177.8 mm sides through its axis. If the mass of the bar is 2027.1 kg, find the relative density of this material.

A. 10.7

B. 9.77

C. 9.77 kg/m³

D. 8.44

E. 8.44 kg/m³

Answer: D

A pile of coal that forms a perfect cone shape has a base area of 24 m² and a height of 15 m. Assuming the pile has 25 percent of void space, and that the density of the coal given is 1400 kg/m³, determine the mass of the coal in this pile.

A pile of coal that forms a perfect cone shape has a base area of 24 m² and a height of 15 m. Assuming the pile has 25 percent of void space, and that the density of the coal given is 1400 kg/m³, determine the mass of the coal in this pile.

A. 12,600 kg

B. 14,700 kg

C. 54,000 kg

D. 126 t

E. 168 t


Answer: D

"Standard conditions" used to compare mass densities of several substance are set at _____ atmosphere pressure.

"Standard conditions" used to compare mass densities of several substance are set at _____ atmosphere pressure.

A. 25°C and 25

B. 20°C and 1

C. 20°C and 0

D. 0°C and 0

E. 0°C and 1


Answer: E

The screw below has a pitch of a screw thread of 10 mm ("two start" thread). The handle is 300 mm long. An effort of 250 N is applied to the handle. If the efficiency of the jack due to the friction within the lifting threads is 50%, how many tonnes can it lift?

The screw below has a pitch of a screw thread of 10 mm ("two start" thread). The handle is 300 mm long. An effort of 250 N is applied to the handle. If the efficiency of the jack due to the friction within the lifting threads is 50%, how many tonnes can it lift?

A. 1 tonne

B. 1.2 tonnes

C. 2.4 tonnes

D. 3.6 tonnes

E. 2.8 tonnes


Answer: B

The ambient pressure is 100.78 kPa. The pressure gauge on a hot water boiler is showing 85 kPa. Determine the absolute pressure under which this boiler is operating.

The ambient pressure is 100.78 kPa. The pressure gauge on a hot water boiler is showing 85 kPa. Determine the absolute pressure under which this boiler is operating.

A. 15.78 kPa

B. 85 kPa

C. 115.325 kPa

D. 135.78 kPa

E. 185.78 kPa


Answer: E

A swimming pool is 4 m deep. When the pool is full of water what is the gage pressure at the bottom?

A swimming pool is 4 m deep. When the pool is full of water what is the gage pressure at the bottom?

A. 4,000 Pa

B. 11 kPa

C. 24.3 kPa

D. 39.24 kPa

E. 140.54 kPa


Answer: D

A solid brass statue has a mass of 20,000 kg. What mass of steel would be required to exactly duplicate the structure?

A solid brass statue has a mass of 20,000 kg. What mass of steel would be required to exactly duplicate the structure?

A. 303.5 kg

B. 18 572 kg

C. 21 347 kg

D. 21 593 kg

E. 20 000 kg


Answer: B

A 5000 litre oil tank contains 60 litres of water. If the water is drained off and replaced with fresh oil of relative density 0.95, what is the change in the mass of the tank's contents?

A 5000 litre oil tank contains 60 litres of water. If the water is drained off and replaced with fresh oil of relative density 0.95, what is the change in the mass of the tank's contents?

A. 4940 kg

B. 4750 kg

C. 60 kg

D. 5 kg

E. 3 kg


Answer: E

A cylindrical tank has its axis vertical. It is 2 m in diameter and its mass is 800 kg. When it is filled to 2 m high with oil, the total mass is 5050 kg. What is the relative density of the oil?

A cylindrical tank has its axis vertical. It is 2 m in diameter and its mass is 800 kg. When it is filled to 2 m high with oil, the total mass is 5050 kg. What is the relative density of the oil?

A. 6.312

B. 6.764 kg/m³

C. 6.764

D. 0.876

E. 0.6764


Answer: E

Specific weight is

Specific weight is

A. A unit used to indicate volume per unit weight

B. A term used in the Imperial System only

C. Equal to the ratio of mass to its force

D. Used to indicate density of a substance compared to the density of water

E. Force per unit of area


Answer: B

A pipe has an inside diameter of 4 cm with a water flow of 5,000 L/hr. What is the velocity of the water?

A pipe has an inside diameter of 4 cm with a water flow of 5,000 L/hr. What is the velocity of the water?

A. 1.1 m/s

B. 2.2 m/s

C. 3.3 m/s

D. 4.4 m/s

E. 5.5 m/s


Answer: A

The "relative density" of a substance refers to the density of:

The "relative density" of a substance refers to the density of:

A. A substance compared to the density of water

B. A substance compared to the density of air at standard conditions

C. A substance compared to the density of gold

D. A substance compared to the density of the same substance at standard conditions

E. Water divided by the density of other substance


Answer: A

A pipe has an inside diameter of 4 cm with an oil flow of 5,000 kg/hr. The relative density of the oil is 0.9. What is the velocity of the oil?

A pipe has an inside diameter of 4 cm with an oil flow of 5,000 kg/hr. The relative density of the oil is 0.9. What is the velocity of the oil?

A. 1.21 m/s

B. 2.45 m/s

C. 3.66 m/s

D. 4.84 m/s

E. 6.05 m/s


Answer: A

The unit of relative density is:

The unit of relative density is:

A. kg/m³

B. lbs/ft³

C. N/m²

D. None

E. kg/cm³


Answer: D

The efficiency of any apparatus is given by the ratio:

The efficiency of any apparatus is given by the ratio:

A. Input divided by output

B. Distance effort moves divided by distance load moves

C. Output divided by input

D. Load divided by effort

E. Load multiplied by effort


Answer: C

The wheel-and-axle system below has dimensions d = 300 mm and R = 1.5 m. If the efficiency of the machine is 90%, find the mechanical advantage of the system.

The wheel-and-axle system below has dimensions d = 300 mm and R = 1.5 m. If the efficiency of the machine is 90%, find the mechanical advantage of the system.

A. 4.5

B. 5

C. 7

D. 9

E. 10


Answer: D

A wheel and axle has a wheel of 60 cm diameter, and an axle of 7.5 cm diameter. Calculate the effort required to raise a mass of 50 kg.

A wheel and axle has a wheel of 60 cm diameter, and an axle of 7.5 cm diameter. Calculate the effort required to raise a mass of 50 kg.

A. 4.5 N

B. 12.26 N

C. 61.31 N

D. 1226 N

E. 3924 N

Answer: C

The ambient pressure is 100.78 kPa. The pressure gauge on a hot water boiler is showing 85 kPa. Determine the absolute pressure under which this boiler is operating.

The ambient pressure is 100.78 kPa. The pressure gauge on a hot water boiler is showing 85 kPa. Determine the absolute pressure under which this boiler is operating.

A. 15.78 kPa

B. 85 kPa

C. 115.325 kPa

D. 135.78 kPa

E. 185.78 kPa


Answer: E

The bending moment at any section in a beam is the algebraic sum of:

The bending moment at any section in a beam is the algebraic sum of:

A. The upward forces and downward forces

B. moments to the left or the right of the section being considered

C. The distributed loads and the concentrated loads

D. The moments at the support

E. All the force couples acting on the beam


Answer: B

Young's Modulus may be applied to which of the following applied loadings?

Young's Modulus may be applied to which of the following applied loadings?

A. Shear

B. Torque

C. Stationary

D. Bending

E. Compression


Answer: E

Three identical bolts are required to carry a total load of 6.75 t. If the stress allowed in the material is 55,900 kPa, calculate the minimum diameter of each bolt.

Three identical bolts are required to carry a total load of 6.75 t. If the stress allowed in the material is 55,900 kPa, calculate the minimum diameter of each bolt.

A. 0.88 mm

B. 22.4 mm

C. 25.4 mm

D. 28.5 mm

E. 66.4 mm


Answer: B

When a simply supported, horizontal beam has a load of 19,620 kN hanging from the center of the beam, each support (ignoring the mass of the beam itself) carries an equivalent mass of:

When a simply supported, horizontal beam has a load of 19,620 kN hanging from the center of the beam, each support (ignoring the mass of the beam itself) carries an equivalent mass of:

A. 900 kg

B. 1000 t

C. 9810 kg

D. 100 t

E. 1000 kg

Answer: B

A steel bar is 4 m long, and has a rectangular cross section of 3 cm x 4 cm. It is in tension from a force of 360 kN. Find the stress induced.

A steel bar is 4 m long, and has a rectangular cross section of 3 cm x 4 cm. It is in tension from a force of 360 kN. Find the stress induced.

A. 300 kPa

B. 300 MPa

C. 120,000 kPa

D. 300,000 kN/cm²

E. None of the above


Answer: B

A perfectly elastic material:

A perfectly elastic material:

A. Shows no sign of strain due to loading when the load is removed

B. Maintains a new length or shape after the load is removed

C. Can only be loaded to the yield point

D. Will take any shape due to elastic ability

E. Can only be loaded to the elastic limit


Answer: A

If the amount that a bolt is stretched when subjected to a load is divided by the original length, the ratio found is classed as:

If the amount that a bolt is stretched when subjected to a load is divided by the original length, the ratio found is classed as:

A. Linear stress

B. Compressive stress

C. Axial stress

D. Linear strain

E. Axial thrust



Answer: D

A beam is simply supported at both ends and carries a concentrated load of 1000 N in the middle. The types of stress that are set up in the beam are:

A beam is simply supported at both ends and carries a concentrated load of 1000 N in the middle. The types of stress that are set up in the beam are:

A. Shear stress and bending stress

B. Compression and tension stress

C. Concentrated stress and shear stress

D. Compression stress and bending stress

E. Tension stress and shear stress


Answer: A

When considering a steel block subjected to a tensile force, we would find the stress in the block by: 1.Using the formula stress equals force divided by the area 2.Using the same formula we use to find stress in a block subjected to a compressive force 3.Using the same formula we use to find the shear stress in a bolt

When considering a steel block subjected to a tensile force, we would find the stress in the block by: 1.Using the formula stress equals force divided by the area 2.Using the same formula we use to find stress in a block subjected to a compressive force 3.Using the same formula we use to find the shear stress in a bolt

A. 1, 2

B. 2, 3

C. 1, 3

D. 1, 2, 3

E. 3


Answer: D

The internal resistance to an external force applied to a body is known as:

The internal resistance to an external force applied to a body is known as:

A. Strain

B. Stress

C. Young's Modulus

D. Ultimate strength

E. Allowable strength

Answer: B

A steel wire 6 mm in diameter is used for hoisting purposes in building construction. If 150 m of the wire is hanging vertically, and a load of 1 kN is being lifted at the lower end of the wire, determine the elongation of the wire. Ignore the mass of the wire itself. Assume that E = 200 GPa.

A steel wire 6 mm in diameter is used for hoisting purposes in building construction. If 150 m of the wire is hanging vertically, and a load of 1 kN is being lifted at the lower end of the wire, determine the elongation of the wire. Ignore the mass of the wire itself. Assume that E = 200 GPa.

A. 106.1 mm

B. 39.78 mm

C. 26.5 mm

D. 10.61 mm

E. 2.65 mm


Answer: C

A diagram that shows the stress caused by forces acting perpendicular to the beam at every cross section along the length of a beam is called the _____ diagram.

A diagram that shows the stress caused by forces acting perpendicular to the beam at every cross section along the length of a beam is called the _____ diagram.

A. Shear

B. Bending moment

C. Compression

D. Tension

E. Torsional


Answer: A

Three identical bolts are required to carry a total load of 6.75 t. If the stress allowed in the material is 55,900 kPa, calculate the minimum diameter of each bolt.

Three identical bolts are required to carry a total load of 6.75 t. If the stress allowed in the material is 55,900 kPa, calculate the minimum diameter of each bolt.

A. 0.88 mm

B. 22.4 mm

C. 25.4 mm

D. 28.5 mm

E. 66.4 mm


Answer: B

The bending moment at any section in a beam is the algebraic sum of:

The bending moment at any section in a beam is the algebraic sum of:

A. The upward forces and downward forces

B. moments to the left or the right of the section being considered

C. The distributed loads and the concentrated loads

D. The moments at the support

E. All the force couples acting on the beam


Answer: B

An I-beam under compressive load is, found to be 0.023 mm shorter than the original length. Given the original length we can find the:

An I-beam under compressive load is, found to be 0.023 mm shorter than the original length. Given the original length we can find the:

A. Compressive stress

B. Tensile stress

C. Linear strain

D. Tensile strain

E. Shearing strain


Answer: C

The maximum stress produced during fracture of a material is its:

The maximum stress produced during fracture of a material is its:

A. Brittleness

B. Ductility

C. Ultimate strength

D. Stiffness

E. Hardness



Answer: C

The magnitude of the moment of a force is equal to force times the:

The magnitude of the moment of a force is equal to force times the:

A. Area

B. Time

C. Pressure

D. Perpendicular distance

E. Circular distance

Answer: D

If the amount that a bolt is stretched when subjected to a load is divided by the original length, the ratio found is classed as:

If the amount that a bolt is stretched when subjected to a load is divided by the original length, the ratio found is classed as:

A. Linear stress

B. Compressive stress

C. Axial stress

D. Linear strain

E. Axial thrust


Answer: D

The maximum allowable stress of a material that has an ultimate strength of 525 MPa and a safety factor of 7 would be:

The maximum allowable stress of a material that has an ultimate strength of 525 MPa and a safety factor of 7 would be:

A. 3675 MPa

B. 367.5 MPa

C. 75 MPa

D. 525 kPa

E. 75 kPa


Answer: C

When considering a steel block subjected to a tensile force, we would find the stress in the block by: 1.Using the formula stress equals force divided by the area 2.Using the same formula we use to find stress in a block subjected to a compressive force 3.Using the same formula we use to find the shear stress in a bolt

When considering a steel block subjected to a tensile force, we would find the stress in the block by: 1.Using the formula stress equals force divided by the area 2.Using the same formula we use to find stress in a block subjected to a compressive force 3.Using the same formula we use to find the shear stress in a bolt

A. 1, 2

B. 2, 3

C. 1, 3

D. 1, 2, 3

E. 3


Answer: D

A steel tube is 7 m long and is 6 cm OD with a wall thickness of 4 mm. It hangs vertically with a load of 400 kg attached to its lower end. If the modulus of elasticity is 210 x 106 kPa, find the stress induced in pipe material.

A steel tube is 7 m long and is 6 cm OD with a wall thickness of 4 mm. It hangs vertically with a load of 400 kg attached to its lower end. If the modulus of elasticity is 210 x 106 kPa, find the stress induced in pipe material.

A. 1.39 MPa

B. 1.47 MPa

C. 3.47 MPa

D. 5.57 MPa

E. 12.49 MPa


Answer: D

A steel bar is 4 m long, and has a rectangular cross section of 3 cm x 4 cm. It is in tension from a force of 360 kN. Find the stress induced.

A steel bar is 4 m long, and has a rectangular cross section of 3 cm x 4 cm. It is in tension from a force of 360 kN. Find the stress induced.

A. 300 kPa

B. 300 MPa

C. 120,000 kPa

D. 300,000 kN/cm²

E. None of the above


Answer: B

By definition, the result of a force moving through a distance is:

By definition, the result of a force moving through a distance is:

A. Power

B. Acceleration

C. Work

D. Moment of force

E. Velocity


Answer: C

A train travels at various speeds between several stations. From the train schedule the following information can be extracted about the different segments of the journey: 8 km traveled in 10 min., 14 km in 12 min., 16 km in 18 min., 12 km in 10 min. The average speed during the whole trip is:

A train travels at various speeds between several stations. From the train schedule the following information can be extracted about the different segments of the journey: 8 km traveled in 10 min., 14 km in 12 min., 16 km in 18 min., 12 km in 10 min. The average speed during the whole trip is:

A. 13.89 km/h

B. 50.0 km/h

C. 60.0 km/h

D. 72.0 km/h

E. 100.0 km/h


Answer: C

Acceleration is:

Acceleration is:

A. The increase of the displacement of a body

B. A body's rate of change of velocity

C. Expressed usually as km/h

D. The rate of change of time

E. The increase of the velocity of a body


Answer: B

A steam turbine has an output of 40 MJ/s. Its power output, in kW is:

A steam turbine has an output of 40 MJ/s. Its power output, in kW is:

A. 11.11 kW

B. 4,000 KW

C. 40,000 kW

D. 24,000 kW

E. 240,000 kW


Answer: C

The work required to move a mass of 20 kg up a vertical distance of 10 m in one minute is:

The work required to move a mass of 20 kg up a vertical distance of 10 m in one minute is:

A. 9.81 J

B. 32.7 J

C. 32.7 kJ

D. 1962 J

E. 115.72 kJ


Answer: D

From what height must a mass of 2 kg fall to have the same amount of kinetic energy as a bullet of 25 g traveling at the speed of 1000 m/s.

From what height must a mass of 2 kg fall to have the same amount of kinetic energy as a bullet of 25 g traveling at the speed of 1000 m/s.

A. 50 m

B. 98.1 m

C. 243.7 m

D. 543.39 m

E. 637.1 m


Answer: E

A word that refers to the change in the position of a body, relative to some reference point is:

A word that refers to the change in the position of a body, relative to some reference point is:

A. Magnitude

B. Displacement

C. Direction

D. Distance

E. Velocity


Answer: B

A flywheel changes speed uniformly from 400 rpm to 100 rpm in 1 minute. What is the angular retardation of the flywheel in rad/s²?

A flywheel changes speed uniformly from 400 rpm to 100 rpm in 1 minute. What is the angular retardation of the flywheel in rad/s²?

A. 0.0833 rad/s²

B. 0.523 rad/s²

C. 0.698 rad/s²

D. 1.0 rad/s²

E. 5.0 rad/s²


Answer: B

Average velocity is determined by:

Average velocity is determined by:

A. V(ave) = v/2

B. V(ave) = u + 2a s²

C. V(ave) = (u + v)/2

D. V(ave) = u - at

E. V(ave) = ut + 1/2 a t²


Answer: C

In order to calculate the power in watts required to lift a 25 kg concrete block to a height of 40 m, you would also need to know the:

In order to calculate the power in watts required to lift a 25 kg concrete block to a height of 40 m, you would also need to know the:

A. Time in seconds

B. Specific gravity of concrete

C. Mass-to-height ratio

D. Atmospheric pressure

E. Volume and density of the block


Answer: A

A steam turbine has an output of 40 MJ/s. Its power output, in kW is:

A steam turbine has an output of 40 MJ/s. Its power output, in kW is:

A. 11.11 kW

B. 4,000 KW

C. 40,000 kW

D. 24,000 kW

E. 240,000 kW


Answer: C

The work required to move a mass of 20 kg up a vertical distance of 10 m in one minute is:

The work required to move a mass of 20 kg up a vertical distance of 10 m in one minute is:

A. 9.81 J

B. 32.7 J

C. 32.7 kJ

D. 1962 J

E. 115.72 kJ


Answer: D

A flywheel changes speed uniformly from 400 rpm to 100 rpm in 1 minute. What is the angular retardation of the flywheel in rad/s²?

A flywheel changes speed uniformly from 400 rpm to 100 rpm in 1 minute. What is the angular retardation of the flywheel in rad/s²?

A. 0.0833 rad/s²

B. 0.523 rad/s²

C. 0.698 rad/s²

D. 1.0 rad/s²

E. 5.0 rad/s²


Answer: B

An airplane travels 1000 km eastwards for 2 hours. Its average speed in m/s is:

An airplane travels 1000 km eastwards for 2 hours. Its average speed in m/s is:

A. 69.44 m/s

B. 138.89 m/s

C. 500 m/s

D. 1000 m/s

E. 3600 m/s


Answer: B

Displacement is:

Displacement is:

A. A vector quantity

B. Speed multiplied by time

C. A scalar quantity

D. Acceleration divided by time

E. Velocity divided by time


Answer: A

By definition, the result of a force moving through a distance is:

By definition, the result of a force moving through a distance is:

A. Power

B. Acceleration

C. Work

D. Moment of force

E. Velocity


Answer: C

A 1 kg pipe wrench is dropped from a height of 25 m. In km/h, its velocity at impact will be:

A 1 kg pipe wrench is dropped from a height of 25 m. In km/h, its velocity at impact will be:

A. 22.15 km/h

B. 25 km/h

C. 30 km/h

D. 61.8 km/h

E. 79.7 km/h


Answer: E

In a speed test, a car traveling at 40 km/h increases its velocity uniformly for 4 seconds, while traveling the controlled distance of 100 m. Its acceleration in m/s² is:

In a speed test, a car traveling at 40 km/h increases its velocity uniformly for 4 seconds, while traveling the controlled distance of 100 m. Its acceleration in m/s² is:

A. 25 m/s²

B. 6.945 m/s²

C. 4.45 m/s²

D. 2.8 m/s²

E. 111.15 m/s²


Answer: B

The potential energy contained in a mass of 20 kg located 15 m above ground level is:

The potential energy contained in a mass of 20 kg located 15 m above ground level is:

A. 2.934 J

B. 300 J

C. 2.943 kJ

D. 30 kJ

E. 300 kJ


Answer: C

Acceleration is:

Acceleration is:

A. The increase of the displacement of a body

B. A body's rate of change of velocity

C. Expressed usually as km/h

D. The rate of change of time

E. The increase of the velocity of a body


Answer: B

A 1 kg pipe wrench is dropped from a height of 25 m. In km/h, its velocity at impact will be:

A 1 kg pipe wrench is dropped from a height of 25 m. In km/h, its velocity at impact will be:

A. 22.15 km/h

B. 25 km/h

C. 30 km/h

D. 61.8 km/h

E. 79.7 km/h


Answer: E

By definition, the result of a force moving through a distance is:

By definition, the result of a force moving through a distance is:

A. Power

B. Acceleration

C. Work

D. Moment of force

E. Velocity


Answer: C

An airplane travels 1000 km eastwards for 2 hours. Its average speed in m/s is:

An airplane travels 1000 km eastwards for 2 hours. Its average speed in m/s is:

A. 69.44 m/s

B. 138.89 m/s

C. 500 m/s

D. 1000 m/s

E. 3600 m/s



Answer: B

In a speed test, a car traveling at 40 km/h increases its velocity uniformly for 4 seconds, while traveling the controlled distance of 100 m. Its acceleration in m/s² is:

In a speed test, a car traveling at 40 km/h increases its velocity uniformly for 4 seconds, while traveling the controlled distance of 100 m. Its acceleration in m/s² is:

A. 25 m/s²

B. 6.945 m/s²

C. 4.45 m/s²

D. 2.8 m/s²

E. 111.15 m/s²



Answer: B

As the acceleration due to gravity is a known constant, the final velocity of a falling body may be found by the formula:

As the acceleration due to gravity is a known constant, the final velocity of a falling body may be found by the formula:

A. v = u² + 2as²

B. v = u + v/2

C. v = u + at

D. v = u²+ 2as

E. v = ut + ½at²


Answer: C

The potential energy contained in a mass of 20 kg located 15 m above ground level is:

The potential energy contained in a mass of 20 kg located 15 m above ground level is:

A. 2.934 J

B. 300 J

C. 2.943 kJ

D. 30 kJ

E. 300 kJ

Answer: C

Acceleration is:

Acceleration is:

A. The increase of the displacement of a body

B. A body's rate of change of velocity

C. Expressed usually as km/h

D. The rate of change of time

E. The increase of the velocity of a body


Answer: B

A steam turbine has an output of 40 MJ/s. Its power output, in kW is:

A steam turbine has an output of 40 MJ/s. Its power output, in kW is:

A. 11.11 kW

B. 4,000 KW

C. 40,000 kW

D. 24,000 kW

E. 240,000 kW


Answer: C

From what height must a mass of 2 kg fall to have the same amount of kinetic energy as a bullet of 25 g traveling at the speed of 1000 m/s.

From what height must a mass of 2 kg fall to have the same amount of kinetic energy as a bullet of 25 g traveling at the speed of 1000 m/s.

A. 50 m

B. 98.1 m

C. 243.7 m

D. 543.39 m

E. 637.1 m


Answer: E

The hammer of a pile driver has a mass of 3000 kg. It falls through a height of 9 m. The hammer's kinetic energy just before impact is:

The hammer of a pile driver has a mass of 3000 kg. It falls through a height of 9 m. The hammer's kinetic energy just before impact is:

A. 27.0 kJ

B. 264.87 kJ

C. 27,000 kJ

D. 243,000 J

E. None of the above


Answer: B

A block of stone of 40 kg is hauled along a horizontal floor by a force inclined 20 degrees to the horizontal. If the coefficient of friction between the stone and the floor is 0.3, determine the effort required to just move the stone from rest.

A block of stone of 40 kg is hauled along a horizontal floor by a force inclined 20 degrees to the horizontal. If the coefficient of friction between the stone and the floor is 0.3, determine the effort required to just move the stone from rest.

A. 157.77 N

B. 140.63 N

C. 117.72 N

D. 112.9 N

E. 84.2 N


Answer: D

A man walks 3.2 km due east and then 4 km in a direction 20° west of south. Find the distance between his final position and his starting point.

A man walks 3.2 km due east and then 4 km in a direction 20° west of south. Find the distance between his final position and his starting point.

A. 3.29 km

B. 4.18 km

C. 4.54 km

D. 5.31 km

E. 5.66 km


Answer: B

Into how many components can a single vector be resolved?

Into how many components can a single vector be resolved?

A. None

B. One

C. Two

D. Four

E. Unlimited


Answer: C

A load of 750 kg just starts to move when the friction angle is 10°. What effort must be applied parallel to the horizontal surface to stop the motion of the block?

A load of 750 kg just starts to move when the friction angle is 10°. What effort must be applied parallel to the horizontal surface to stop the motion of the block?

A. 7245.72 N

B. 1478.22 N

C. 1297.33 N

D. 1277.62 N

E. 1124.35 N


Answer: C

A body with a gravitational force of 2000 N is pulled along a horizontal surface at constant speed by a rope, which makes an angle of 20° above the horizontal. If the force on the rope is 150 N, the coefficient of sliding friction is:

A body with a gravitational force of 2000 N is pulled along a horizontal surface at constant speed by a rope, which makes an angle of 20° above the horizontal. If the force on the rope is 150 N, the coefficient of sliding friction is:

A. 0.0257

B. 0.0275

C. 0.0275 N

D. 0.0656

E. 0.0704


Answer: E

Find the value and applied angle of the least force required to move a vessel, if the mass of the vessel is 1650 kg and the coefficient of friction is 0.49.

Find the value and applied angle of the least force required to move a vessel, if the mass of the vessel is 1650 kg and the coefficient of friction is 0.49.

A. 7122.31 N, 26.10 degrees

B. 5562.52 N, 31.47 degrees

C. 5522.52 N, 31.47 degrees

D. 4098.52 N, 22.22 degrees

E. 726.03 N, 25.10 degrees


Answer: A

A sliding face of a slide valve of a steam engine is 150 mm by 300 mm, and the steam pressure on the back of the valve is 1200 kN/m². If the coefficient of friction is 0.02, what is the force required to move the valve?

A sliding face of a slide valve of a steam engine is 150 mm by 300 mm, and the steam pressure on the back of the valve is 1200 kN/m². If the coefficient of friction is 0.02, what is the force required to move the valve?

A. 2400 N

B. 1800 N

C. 1080 N

D. 960 N

E. 840 N


Answer: C

A wooden box is loaded and its mass is 40 kg. A force of 150 N that just sets it in motion pulls it horizontally. Determine the coefficient of friction.

A wooden box is loaded and its mass is 40 kg. A force of 150 N that just sets it in motion pulls it horizontally. Determine the coefficient of friction.

A. 3.75 N

B. 2.616

C. 0.382

D. 0.382 N

E. 0.368


Answer: C

A displacement of 9 m north of point A, and another of 6 m west of point A can be added to produce a resultant displacement of:

A displacement of 9 m north of point A, and another of 6 m west of point A can be added to produce a resultant displacement of:

A. 3 m at 34 deg W of N

B. 10 m at 34 deg.N of W

C. 10.8 m at 56 deg. N of W

D. 12.5 m N of W

E. 15 m at 44 deg. N of W


Answer: C

A load of 750 kg just starts to move when the friction angle is 10°. What effort must be applied parallel to the horizontal surface to stop the motion of the block?

A load of 750 kg just starts to move when the friction angle is 10°. What effort must be applied parallel to the horizontal surface to stop the motion of the block?

A. 7245.72 N

B. 1478.22 N

C. 1297.33 N

D. 1277.62 N

E. 1124.35 N


Answer: C

A man walks 3.2 km due east and then 4 km in a direction 20° west of south. Find the distance between his final position and his starting point.

A man walks 3.2 km due east and then 4 km in a direction 20° west of south. Find the distance between his final position and his starting point.

A. 3.29 km

B. 4.18 km

C. 4.54 km

D. 5.31 km

E. 5.66 km


Answer: B

A body can be put into equilibrium by applying an additional force equal in magnitude but opposite in direction to the:

A body can be put into equilibrium by applying an additional force equal in magnitude but opposite in direction to the:

A. Resultant

B. Scalar

C. Equilibrant

D. Component

E. Element


Answer: A

Find the value and applied angle of the least force required to move a vessel, if the mass of the vessel is 1650 kg and the coefficient of friction is 0.49.

Find the value and applied angle of the least force required to move a vessel, if the mass of the vessel is 1650 kg and the coefficient of friction is 0.49.

A. 7122.31 N, 26.10 degrees

B. 5562.52 N, 31.47 degrees

C. 5522.52 N, 31.47 degrees

D. 4098.52 N, 22.22 degrees

E. 726.03 N, 25.10 degrees


Answer: A

A man has a mass of 70 kg. What is the magnitude of the largest mass he can pull by a horizontal rope along a horizontal floor, if the coefficient of friction between the mass and the floor is 0.23, and that between his boot soles and the floor is 0.5?

A man has a mass of 70 kg. What is the magnitude of the largest mass he can pull by a horizontal rope along a horizontal floor, if the coefficient of friction between the mass and the floor is 0.23, and that between his boot soles and the floor is 0.5?

A. 134.3 kg

B. 152.2 kg

C. 170 kg

D. 102.2 kg

E. 343.4 kg


Answer: B

The force that is equal in magnitude but opposite in direction to the resultant force is called the:

The force that is equal in magnitude but opposite in direction to the resultant force is called the:

A. Component

B. Element

C. Displacement

D. Equilibrant

E. Impedance


Answer: D

A refrigerator with a mass of 150 kg sits on a perfectly level surface. It is pushed by a force of 350 N, acting upward at 30 degrees to the horizontal. If the coefficient of friction between the refrigerator and the surface is 0.25, what will happen to the refrigerator?

A refrigerator with a mass of 150 kg sits on a perfectly level surface. It is pushed by a force of 350 N, acting upward at 30 degrees to the horizontal. If the coefficient of friction between the refrigerator and the surface is 0.25, what will happen to the refrigerator?

A. The refrigerator will start moving maintaining a steady speed as kinetic friction increases

B. The refrigerator will slide and continue to accelerate

C. The refrigerator will slide at a constant velocity

D. The refrigerator will tip

E. The refrigerator will not move


Answer: E

One of the conditions of a force system in equilibrium is:

One of the conditions of a force system in equilibrium is:

A. There are no forces acting parallel to each other

B. The resultant of the forces produce an acceleration

C. The sum of the forces to the left must equal the sum of the forces to the right

D. All the forces in the system must act to the same direction

E. None of the above


Answer: C

Find the value and applied angle of the least force required to move a vessel, if the mass of the vessel is 1650 kg and the coefficient of friction is 0.49.

Find the value and applied angle of the least force required to move a vessel, if the mass of the vessel is 1650 kg and the coefficient of friction is 0.49.

A. 7122.31 N, 26.10 degrees

B. 5562.52 N, 31.47 degrees

C. 5522.52 N, 31.47 degrees

D. 4098.52 N, 22.22 degrees

E. 726.03 N, 25.10 degrees


Answer: A

The force of friction always:

The force of friction always:

A. Goes along with the applied force

B. Goes against the applied force

C. Depends on the contact area between two surfaces

D. Is harmful to the operation of machinery

E. Exists even when there is no applied force


Answer: B

A man has a mass of 70 kg. What is the magnitude of the largest mass he can pull by a horizontal rope along a horizontal floor, if the coefficient of friction between the mass and the floor is 0.23, and that between his boot soles and the floor is 0.5?

A man has a mass of 70 kg. What is the magnitude of the largest mass he can pull by a horizontal rope along a horizontal floor, if the coefficient of friction between the mass and the floor is 0.23, and that between his boot soles and the floor is 0.5?

A. 134.3 kg

B. 152.2 kg

C. 170 kg

D. 102.2 kg

E. 343.4 kg


Answer: B

The force that is equal in magnitude but opposite in direction to the resultant force is called the:

The force that is equal in magnitude but opposite in direction to the resultant force is called the:

A. Component

B. Element

C. Displacement

D. Equilibrant

E. Impedance


Answer: D

A body having a mass of 50.97 kg is pulled along a horizontal flat surface at a constant speed by a force of 180 N, which makes an angle of +30° with the horizontal. Find the coefficient of kinetic friction for the surfaces.

A body having a mass of 50.97 kg is pulled along a horizontal flat surface at a constant speed by a force of 180 N, which makes an angle of +30° with the horizontal. Find the coefficient of kinetic friction for the surfaces.

A. 0.311

B. 1.441 N

C. 0.896

D. 0.38 N

E. 0.38


Answer: E

A load of 750 kg just starts to move when the friction angle is 10°. What effort must be applied parallel to the horizontal surface to stop the motion of the block?

A load of 750 kg just starts to move when the friction angle is 10°. What effort must be applied parallel to the horizontal surface to stop the motion of the block?

A. 7245.72 N

B. 1478.22 N

C. 1297.33 N

D. 1277.62 N

E. 1124.35 N


Answer: C

A trapezoid has parallel sides of 5 m and 8 m, and a height of 4 m. Find the area.

A trapezoid has parallel sides of 5 m and 8 m, and a height of 4 m. Find the area.

A. 17 m²

B. 21 m²

C. 26 m²

D. 30 m²

E. 36 m²


Answer: C

A rhomboid is a plane figure that has four (4) sides, with:

A rhomboid is a plane figure that has four (4) sides, with:

A. All sides parallel

B. Opposite sides parallel and all angles equal

C. Opposite sides parallel and opposite angles equal

D. Opposite sides parallel and equal and opposite angles equal

E. Two opposite sides parallel, the other two sides not


Answer: C

The major axis of an ellipse is 38 cm long and the area of the ellipse is 418 cm². What is the length of the minor axis?

The major axis of an ellipse is 38 cm long and the area of the ellipse is 418 cm². What is the length of the minor axis?

A. 7 cm

B. 14 cm

C. 16 cm

D. 28 cm

E. 32 cm


Answer: B

An octagon has sides 4 cm long. How much larger is its area than a circle with a radius which is also 4 cm long?

An octagon has sides 4 cm long. How much larger is its area than a circle with a radius which is also 4 cm long?

A. 8.66 cm²

B. 18.01 cm²

C. 22.67 cm²

D. 27.01 cm²

E. 64.72 cm²


Answer: D

A triangle with all three sides the same length is called a/an __________ triangle.

A triangle with all three sides the same length is called a/an __________ triangle.

A. Isosceles

B. Scalene

C. Acute

D. Equilateral

E. Obtuse


Answer: D

A trapezoid is a plane figure, which has four (4) sides, and:

A trapezoid is a plane figure, which has four (4) sides, and:

A. All sides are parallel

B. 2 opposite sides are parallel but unequal in length

C. 2 opposite sides are parallel and only opposite angles are equal

D. Opposite sides are parallel and equal, and opposite angles are equal

E. None of the sides are parallel


Answer: B

A triangle has each side equal to 11 m. What is its area and height?

A triangle has each side equal to 11 m. What is its area and height?

A. A = 42.76 m2, h = 6.00 m

B. A = 52.39 m2, h = 9.53 m

C. A = 66.38 m2, h = 12.02 m

D. A = 68.39 m2, h = 12.24 m

E. A = 121 m2, h = 11 m


Answer: B

A triangle in which all three sides (a, b, c) are different lengths, is called a/an ___________ triangle.:

A triangle in which all three sides (a, b, c) are different lengths, is called a/an ___________ triangle.:

A. Isosceles

B. Scalene

C. Equilateral

D. Unilateral

E. Right


Answer: B

A trapezoid has parallel sides of 5 m and 8 m, and a height of 4 m. Find the area.

A trapezoid has parallel sides of 5 m and 8 m, and a height of 4 m. Find the area.

A. 17 m²

B. 21 m²

C. 26 m²

D. 30 m²

E. 36 m²


Answer: C

An octagon has sides 4 cm long. How much larger is its area than a circle with a radius which is also 4 cm long?

An octagon has sides 4 cm long. How much larger is its area than a circle with a radius which is also 4 cm long?

A. 8.66 cm²

B. 18.01 cm²

C. 22.67 cm²

D. 27.01 cm²

E. 64.72 cm²


Answer: D

A cylindrical tank with a vertical axis is 0.6 m in diameter. The oil level falls 20 cm in 17 days. Calculate the quantity of oil used per day in litres.

A cylindrical tank with a vertical axis is 0.6 m in diameter. The oil level falls 20 cm in 17 days. Calculate the quantity of oil used per day in litres.

A. 1.662 litres/day

B. 2.236 litres/day

C. 3.325 litres/day

D. 3.318 litres/day

E. 16.632 litres/day


Answer: C

A reinforced concrete beam requires a cross-sectional area of reinforcing steel equal to 25 cm². If 2 cm diameter steel rods are used, how many will be required?

A reinforced concrete beam requires a cross-sectional area of reinforcing steel equal to 25 cm². If 2 cm diameter steel rods are used, how many will be required?

A. 6 rods

B. 7 rods

C. 8 rods

D. 10 rods

E. 12 rods


Answer: C

An isosceles triangle has an area of 121 m² and a base length of 13 m. What is the vertical height of this (isosceles) triangle?

An isosceles triangle has an area of 121 m² and a base length of 13 m. What is the vertical height of this (isosceles) triangle?

A. 9.23 m

B. 13.33 m

C. 15.78 m

D. 16.63 m

E. 18.62 m


Answer: E

What is the area of a triangle whose sides measure 4 km, 5 km and 7 km?

What is the area of a triangle whose sides measure 4 km, 5 km and 7 km?

A. 9.80 km²

B. 10.78 km²

C. 20.00 km²

D. 35 km²

E. 140 km²


Answer: A

An equilateral triangle has an area of 63.92 m². What is the height of this triangle?

An equilateral triangle has an area of 63.92 m². What is the height of this triangle?

A. 49.20 m

B. 40.12 m

C. 23.15 m

D. 10.52 m

E. 9.15 m


Answer: D

Calculate the number of 8 cm diameter tubes that can be attached to a circular tube sheet of a heat exchanger that is 1.0 m in diameter. Assume that 50% of the sheet area is used for spacing between the tubes.

Calculate the number of 8 cm diameter tubes that can be attached to a circular tube sheet of a heat exchanger that is 1.0 m in diameter. Assume that 50% of the sheet area is used for spacing between the tubes.

A. 72

B. 78

C. 88

D. 98

E. 156


Answer: B

A triangle has each side equal to 11 m. What is its area and height?

A triangle has each side equal to 11 m. What is its area and height?

A. A = 42.76 m2, h = 6.00 m

B. A = 52.39 m2, h = 9.53 m

C. A = 66.38 m2, h = 12.02 m

D. A = 68.39 m2, h = 12.24 m

E. A = 121 m2, h = 11 m


Answer: B

Given that one side of a triangle is equal to 8 m, the base is equal to b m and trhe height is 4 m, the area of this triangle is equal to:

Given that one side of a triangle is equal to 8 m, the base is equal to b m and trhe height is 4 m, the area of this triangle is equal to:

A. 16 m²

B. 32 m²

C. 8b m²

D. 4b m²

E. 2b m²


Answer: E

An octagon has sides 4 cm long. How much larger is its area than a circle with a radius which is also 4 cm long?

An octagon has sides 4 cm long. How much larger is its area than a circle with a radius which is also 4 cm long?

A. 8.66 cm²

B. 18.01 cm²

C. 22.67 cm²

D. 27.01 cm²

E. 64.72 cm²


Answer: D

A cylindrical tank with a vertical axis is 0.6 m in diameter. The oil level falls 20 cm in 17 days. Calculate the quantity of oil used per day in litres.

A cylindrical tank with a vertical axis is 0.6 m in diameter. The oil level falls 20 cm in 17 days. Calculate the quantity of oil used per day in litres.

A. 1.662 litres/day

B. 2.236 litres/day

C. 3.325 litres/day

D. 3.318 litres/day

E. 16.632 litres/day


Answer: C

One radian is equal to:

One radian is equal to:

A. 6.28 degrees

B. 2 radii

C. 57.3 degrees

D. 360 degrees

E. One radius.


Answer: C

A ladder 7.5 m long leans against a wall, and is inclined at 70 degrees to the ground. How far from the wall is the foot of the ladder?

A ladder 7.5 m long leans against a wall, and is inclined at 70 degrees to the ground. How far from the wall is the foot of the ladder?

A. 7.14 m

B. 7.04 m

C. 3.57 m

D. 2.57 m

E. 1.97 m.


Answer: D

The top end of a 12 m long ladder rests on a vertical wall. The foot of the ladder is 3 m away from the base of the wall. Find the angle of inclination of the ladder.

The top end of a 12 m long ladder rests on a vertical wall. The foot of the ladder is 3 m away from the base of the wall. Find the angle of inclination of the ladder.

A. 14.48 degrees

B. 75.52 degrees

C. 78.93 degrees

D. 80.87 degrees

E. 85.00 degrees.



Answer: B

The lower end of a 12 m ladder is 3 m away from the wall. Find the height on the wall where the top of the ladder touches.

The lower end of a 12 m ladder is 3 m away from the wall. Find the height on the wall where the top of the ladder touches.

A. 9.83 m

B. 10.50 m

C. 11.32 m

D. 11.62 m

E. 11.79 m.

Answer: D

Referring to the triangle ABC below, the ratio of opposite side/adjacent side (b/a) for angle B is called the:

Referring to the triangle ABC below, the ratio of opposite side/adjacent side (b/a) for angle B is called the:

A. Sine of angle B or Sin B

B. Cosine of angle B or Cos B

C. Secant of angle B or Sec B

D. Tangent of angle B or Tan B

E. Cotangent of angle B or Cot B.


Answer: D

A packaged boiler is to be unloaded from a flat car. The bed of the flat car is 2 m above the ground. What length of skids is necessary if the skids are to make an angle of 25 degrees with the ground?

A packaged boiler is to be unloaded from a flat car. The bed of the flat car is 2 m above the ground. What length of skids is necessary if the skids are to make an angle of 25 degrees with the ground?

A. 2.21 m

B. 3.12 m

C. 4.29 m

D. 4.73 m

E. 5.73 m.


Answer: D

A tire that turned two and three quarter (2 ¾) revolutions has turned an equivalent of ___________ radians.

A tire that turned two and three quarter (2 ¾) revolutions has turned an equivalent of ___________ radians.

A. 6.28

B. 8.64

C. 17.28

D. 171.29

E. 2.75


Answer: C

In the given triangle, calculate the ratio of BC to AC, when angle ADC = 40 degrees, angle BDC = 20 degrees, angle ACD = 90 degrees, and side DC = 8m.

In the given triangle, calculate the ratio of BC to AC, when angle ADC = 40 degrees, angle BDC = 20 degrees, angle ACD = 90 degrees, and side DC = 8m.

A. 0.351

B. 0.362

C. 0.434

D. 0.474

E. 0.5.


Answer: C

In the following triangle, what is the value of tan A ?

In the following triangle, what is the value of tan A ?

A. 1.33

B. 0.80

C. 0.75

D. 0.6

E. 1.67


Answer: A

In the following right triangle, find the value of angle A, if a = 2 m and b = 6 m.

In the following right triangle, find the value of angle A, if a = 2 m and b = 6 m.

A. 15.21 degrees

B. 16.25 degrees

C. 17.47 degrees

D. 18.43 degrees

E. 22.43 degrees.


Answer: D

The lower end of a 12 m ladder is 3 m away from the wall. Find the height on the wall where the top of the ladder touches.

The lower end of a 12 m ladder is 3 m away from the wall. Find the height on the wall where the top of the ladder touches.

A. 9.83 m

B. 10.50 m

C. 11.32 m

D. 11.62 m

E. 11.79 m.


Answer: D

Which of the following is an acute angle?

Which of the following is an acute angle?

A. 270 degrees

B. 350 degrees

C. 109 degrees 13 minutes 45 seconds

D. 186 degrees 30 minutes 59 seconds

E. 45 degrees.


Answer: E

Refer to the triangle below. Pythagoras' Theorem for this triangle may be stated as:

Refer to the triangle below. Pythagoras' Theorem for this triangle may be stated as:

A. b² = c² + a²

B. c² = a² - b²

C. c² = a² + b²

D. a² = c² + b²

E. c² = b² - a²


Answer: C

Referring to the triangle ABC below, the ratio of: adjacent side / hypotenuse side, for angle A, is called the:

Referring to the triangle ABC below, the ratio of: adjacent side / hypotenuse side, for angle A, is called the:

A. Sine of angle A or Sin A

B. Cosine of angle A or Cos A

C. Secant of angle A or Sec A

D. Tangent of angle A or Tan A

E. Cotangent of angle A or Cot A.


Answer: B

Referring to the triangle ABC below, the ratio of: adjacent side / hypotenuse side, for angle A, is called the:

Referring to the triangle ABC below, the ratio of: adjacent side / hypotenuse side, for angle A, is called the:

A. Sine of angle A or Sin A

B. Cosine of angle A or Cos A

C. Secant of angle A or Sec A

D. Tangent of angle A or Tan A

E. Cotangent of angle A or Cot A.

Answer: B

In the following triangle, find the value of Cos B and its corresponding angle:

In the following triangle, find the value of Cos B and its corresponding angle:

A. 0.75, 48.59 degrees

B. 0.80, 36.87 degrees

C. 1.33, 48.60 degrees

D. 0.6, 36.87 degrees

E. 1.67, 53.22 degrees.


Answer: B

The lower end of a 12 m ladder is 3 m away from the wall. Find the height on the wall where the top of the ladder touches.

The lower end of a 12 m ladder is 3 m away from the wall. Find the height on the wall where the top of the ladder touches.

A. 9.83 m

B. 10.50 m

C. 11.32 m

D. 11.62 m

E. 11.79 m.


Answer: D

Referring to angle A in the figure below, side "a" is called the:

Referring to angle A in the figure below, side "a" is called the:

A. Hypotenuse

B. Adjacent

C. Opposite

D. Reciprocal

E. Median.


Answer: C

In the following triangle, what is the value of sin B and what is the size of the angle B?

In the following triangle, what is the value of sin B and what is the size of the angle B?

A. 0.75, 48.59 degrees

B. 0.80, 53.13 degrees

C. 1.33, 48.6 degrees

D. 0.6, 36,87 degrees

E. 1.67, 53.32 degrees


Answer: D

A ladder 7.5 m long leans against a wall, and is inclined at 70 degrees to the ground. How far from the wall is the foot of the ladder?

A ladder 7.5 m long leans against a wall, and is inclined at 70 degrees to the ground. How far from the wall is the foot of the ladder?

A. 7.14 m

B. 7.04 m

C. 3.57 m

D. 2.57 m

E. 1.97 m.


Answer: D

Referring to the triangle ABC below, the ratio of opposite side/adjacent side (b/a) for angle B is called the:

Referring to the triangle ABC below, the ratio of opposite side/adjacent side (b/a) for angle B is called the:

A. Sine of angle B or Sin B

B. Cosine of angle B or Cos B

C. Secant of angle B or Sec B

D. Tangent of angle B or Tan B

E. Cotangent of angle B or Cot B.

Answer: D

Which of the following is an acute angle?

Which of the following is an acute angle?

A. 270 degrees

B. 350 degrees

C. 109 degrees 13 minutes 45 seconds

D. 186 degrees 30 minutes 59 seconds

E. 45 degrees.


Answer: E

In the following right triangle, find the value of angle A, if a = 2 m and b = 6 m.

In the following right triangle, find the value of angle A, if a = 2 m and b = 6 m.

A. 15.21 degrees

B. 16.25 degrees

C. 17.47 degrees

D. 18.43 degrees

E. 22.43 degrees.


Answer: D

Reflex angles are greater than:

Reflex angles are greater than:

A. 45 degrees

B. 90 degrees

C. 120 degrees

D. 180 degrees

E. 270 degrees.


Answer: D

Rearranging an equation to isolate the unknown is called:

Rearranging an equation to isolate the unknown is called:

A. Isolating.

B. Interpolating.

C. Squaring.

D. Transposing.

E. Solving.


Answer: D

What is the value of X in the following fractional equation: (x/2) + (3x/4) = (4.5/3)

What is the value of X in the following fractional equation:
(x/2) + (3x/4) = (4.5/3)

A. 0.83

B. 1.2

C. 1.5

D. 1.66

E. 2.0.


Answer: B

Using the formulas, F = (9/5)C + 32 and K = C + 273, convert 68o Fahrenheit to Kelvin.

Using the formulas, F = (9/5)C + 32 and K = C + 273, convert 68o Fahrenheit to Kelvin.

A. 0 K

B. 20 K

C. 32 K

D. 273 K

E. 293 K.


Answer: E

What number has 13.4146 as its natural logarithm?

What number has 13.4146 as its natural logarithm?

A. 1.3415

B. 2.5963

C. 259.63

D. 669.71

E. 669709.96.


Answer: E

The natural or Naperian logarithm of 0.00478 is:

The natural or Naperian logarithm of 0.00478 is:

A. -5.3433

B. -3.0407

C. -2.3205

D. 2.3205

E. 5.3433.

Answer: A

In the expression 4² = 16, the number '4' is called the _____ of 16.

In the expression 4² = 16, the number '4' is called the _____ of 16.

A. Square root.

B. Cube root.

C. Square.

D. Cube.

E. Multiplicand.


Answer: A

Find 'u' if v² = u² + 2as, given that v = 34 m/s, a = 9.81 m/s², and s = 8 m.

Find 'u' if v² = u² + 2as, given that v = 34 m/s, a = 9.81 m/s², and s = 8 m.

A. 31.6 m/s

B. 36.2 m/s

C. 1334.6 m/s

D. 999 m/s

E. 2668.3 m/s.


Answer: A

Find log N, if ln N = 5.824

Find log N, if ln N = 5.824

A. 2.529

B. 2.925

C. 25.305

D. 29.259

E. 2530.


Answer: A

What is the value of D in the following equation: 0.005 + D = 0.0055

What is the value of D in the following equation:
0.005 + D = 0.0055

A. 0.025

B. 0.0005

C. 0.06

D. 1

E. (1 - 0.055 - 0.005).


Answer: B

The common and Naperian logarithms for the number 272 are:

The common and Naperian logarithms for the number 272 are:

A. 1.4346, 3.3032

B. 2.4346, 5.6058

C. 3.4345, 7.9084

D. 4.4345, 7.9084

E. 5.4345, 7.9084.


Answer: B

A number taken to the third power is said to be?

A number taken to the third power is said to be?

A. Squared.

B. Cubed.

C. Tripled.

D. Multiplied by three.

E. A cube root.


Answer: B

Using the formulas, F = (9/5)C + 32 and K = C + 273, convert 68o Fahrenheit to Kelvin.

Using the formulas, F = (9/5)C + 32 and K = C + 273, convert 68o Fahrenheit to Kelvin.

A. 0 K

B. 20 K

C. 32 K

D. 273 K

E. 293 K.


Answer: E