Work and Energy MCQs Qs and Numerical

Work and Energy MCQs Qs and Numerical (School)

For more Physics Quizzes Notes and Numerical:

MCQs

1. The work done will be zero when the angle between the force and the distance is:

1. 45^o
2. 60^o
3. 90^o ANS
4. 180^o

2. If the direction of motion of the force is perpendicular to the direction of motion of the body, then work done will be:

1. maximum
2. minimum
3. zero
4. none of these

3. If the velocity of a body becomes double, then its kinetic energy will be:

1. remain the same
2. become double
3. becomes four times
4. become half

4. The work done in lifting a brick of mass 2kg through a height of 5m above ground will be:

1. 2.5 J
2. 10 J
3. 50 J
4. 100 J ANS

5. The kinetic energy of a body of mass 2 kg is 25 J. Its speed is:

1. 4 ms^-1 ANS
2. 12.5 ms^-1
3. 25 ms^-1
4. 50 ms^-1

6. Which one of the following converts light energy into electrical energy?

1. Electric bulb
2. Electric generator
3. Photocell
4. Electric cell

7. When a body is lifted through a height h, the work done on it appears in the form of its:

1. Kinetic energy
2. Potential energy
3. Elastic potential energy
4. Geothermal energy

8. The energy stored in coal is:

1. Heat energy
2. Kinetic energy
3. Chemical energy
4. Nuclear energy

9. The energy stored in a dam is:

1. Electric energy
2. Potential energy
3. Kinetic energy
4. Thermal energy

10. In Einstein's mass-energy equation, c is:

1. Speed of sound
2. Speed of light
3. Speed of electrons
4. Speed of Earth

11. Power is equal to:

1. W / t²
2. W² / t
3. W / t ANS
4. W x t

12. Stretched bow has type of energy:

1. Kinetic energy
2. Heat energy
3. Potential energy
4. Elastic potential energy

13. One horse power is equal to:

1. 746 W ANS
2. 749 W
3. 764 W
4. 794 W

14. Solar cells are also known as:

1. Electric cell
2. Photo cell
3. Sun cells
4. Nuclear cells

15. Rate of doing work is called:

1. Energy
2. Torque
3. Power
4. Momentum

16. Work is equal to:

1. F . S ANS
2. F . v
3. F / S
4. S / F

17. A body possess __ if it is capable to do work.

1. Energy
2. Power
3. Force
4. All

18. An ideal system gives output:

1. 50%
2. 65%
3. 70%
4. 100% ANS

19. Fossil fuels are usually:

1. Carbon dioxide
2. Hydrogen
3. Hydrocarbons
4. Calcium

Question Answers

SQs

Q1. Define work. What is its SI unit? Ans:

Work: "Work is done when force acting on a body displaces it in the direction of a force".

Work is a scalar quantity. It depends on the force acting on a body, displacement of the body and the angle between them.

SI unit: In SI unit of work is joule (J). It is defined as "The amount of work is one joule when a force of one newton displaces a body through one metre in the direction of force".

Thus 1J=1Nx I m

Joule is a small unit of work. Its bigger units are:

1 kilo joule (kJ) = 1000 J = 10³J

1 mega joule (MJ) =1000,000 J = 10⁶J

Q2. When does a force do work? Explain.

Ans. In Physics, work is said to be done when a force acts on a body and moves it in the direction of the force. Greater is the force acting on the body longer is the distance moved by it, larger would be the work done. Work is the product of force F and displacement S in the direction of force.

Work done = Force x displacement

W = FxS

Q3. Why do we need energy?

Ans: We always need energy to do any type of work, The energy has an important and fundamental concept in science. It links almost all the natural phenomena. We say that a body has energy when it has the ability to do work. e.g. water running down the stream has the ability to do work, so it possesses energy. The energy of running water can be used to run water mills or water turbines. Our body gets energy stored in the food we take to perform various activities.

Q4. Define energy, give two types of mechanical energy.

Ans. Energy:- "The ability of a body to do work is called energy". Mechanical energy possessed by a body is of two types: kinetic energy and potential energy. Energy is a scalar quantity.

Q5. Define K.E. and derive its relation.

Ans. Kinetic Energy:- "The energy possessed a body due to its motion is called its kinetic energy".

Derivation:- Consider a body of mas m moving with velocity 'v'. The body after moving through some distance 'S' due to some opposing force such as force friction acting on it. The body possesses kinetic energy and is capable to do work against opposing force F until all of its kinetic energy is used up.

K.E. = FS... (1)

v_ị = v

As v_f = 0

F = ma

As a = -F / m

Since motion of object is opposed, hence, 'a' is negative.

Using 3rd equation of motion:

2aS = v_f²- v_i²

2 (-F/m) S = (0)² -(v)²

FS = 1/2 mv² .. (2)

From Eq. 1 and 2 we get

K.E. = 1/2 mv² (3)

Q6. Define potential energy and derive its relation.

Ans. Potential Energy:- "The energy possessed by a body due to its position is known potential energy".

Derivation:- Let a body of mass m be raised up through height h from the ground. The body will acquire potential energy equal to the work done in lifting it to height h.

Thus Potential energy P.E. = Fxh

= w x h As F = w

(Here weight of the body = w = mg)

So, P.E = mgh

Thus, the potential energy possessed by the body with respect to the ground is mgh and is equal to the work in lifting it to height h.

Q7. Why fossil fuels are called non- renewable sources of energy?

Ans. Fossil fuels took million of years for their formation and they cannot be generated artificially in the short time so they are known as non-renewable resources. We are using fossil fuels at a very fast rate. Their use is increasing day by day to meet our energy needs. If we continue to use them at present rate, they will soon be exhausted. Once their supply is exhausted, the world would face serious energy crisis. Thus, fossil fuels would not be able to meet our future energy needs. This would cause serious social and economical problems for countries like us. Therefore, we must use them wisely and at the same time develop new energy sources for our future survival.

Q8. Which form of energy is most preferred and why?

Ans. Solar energy is more preferable because It can directly obtain from Sun and it does not have any type of pollution in it. It is also Cheaper and renewable source of energy.

Q9. How is energy converted from one form to another? Explain. 

Ans. "Energy cannot be destroyed, but it can be converted into some other forms of energy".

i. During the rubbing of our hands we use muscular energy in rubbing hands as a result heat is produced. In the process of rubbing hands, mechanical energy is converted into heat energy.

ii. Processes in nature are the result of energy changes.

Example:- Heat energy from the Sun is taken up by water in the oceans. This increases the thermal energy. Thermal energy causes water to evaporate from the surface to form water vapours. These vapours rise up and form clouds. As they cool down, they form water drops and fall down as rain. Potential energy changes to kinetic energy as the rain falls. This rain water may reach a lake or a dam. As the rain water flows down, its kinetic energy changes into thermal energy while parts of the kinetic energy of flowing water is used to wash away soil particles of rocks known as soil erosion. During the interconversion of energy, energy from one form changes to another form but the total energy at any time remains constant.

Q10. Name the five devices that convert electrical energy into mechanical energy.

Ans.

1. Electric motor
2. Washing Machine
3. Electric vibrator
4. Electric fan
5. Lifts in the buildings

Q11. Name a device that converts. mechanical energy into electrical energy.

Ans. A.C generator converts the mechanical energy into electrical energy.

Q12. What is meant by the efficiency of a system?

Ans. "Efficiency of a system is the ratio of required form of energy obtained from a system as output to the total energy given to it as input."

Q13. How can you find the efficiency of a system?

Ans. Efficiency of the system can be found by using the formula:

% Efficiency = (required form of output / total input energy) x 100

Q14. What is meant by the term power?

Ans. Power is defined as the "rate of doing work" Mathematically,

Power = P= Work done / Time Taken

P = W / t

Since work is a scalar quantity, therefore, power is also a scalar quantity. Its unit is watt.

Q15. Define watt.

Ans. "The power of a body is one watt if it does work at the rate of 1 joule per second (1 Js^-1)"

Bigger units of power are kilowatt (kW) megawatt (MW) etc.

1 kW = 1000 W

1 MW = 1000,000W = 10⁶W

1 horse power = 1 hp = 746W

Conceptual Qs

Q1. Can a centripetal force ever do work on an object? Explain.

Answer: No, centripetal force does not do work because the force acting on the object and instantaneous displacement of the object are always perpendicular to each other as shown in the figure. So;

W = FS cosθ = FS cos90° = FS(0) = 0 J

The centripetal force allows the object to follow the circular trajectory. The centripetal force is directed towards the center while the tangential velocity of the object is perpendicular to the direction of action of force at every point. Hence no work can be done by it.

Q2. What happens to the kinetic energy of a bullet when it penetrates into a sandbag?

Answer: When a bullet of mass ‘m’ is moving with velocity ‘v’ it possesses kinetic energy given by,

KE = $\frac{1}{2}{mv^2}$

When this bullet hits the sandbag, it penetrates into the sandbag and comes to rest after penetrating into it for some distance. When it comes to rest, the final velocity is 0 m/s.

The kinetic energy possessed by the bullet as given in the above equation is exhausted mostly in the work done against the resistance offered by the sandbag while penetrating into it. Some part of the kinetic energy may also have lost as heat and sound.

Q3. A meteor enters into earth’s atmosphere and burns. What happens to its kinetic energy?

Answer: A meteor has both potential and kinetic energy before entering the atmosphere of the Earth. As it enters and falls towards the surface of the Earth, frictional heating occurs, caused by the collision with the molecules in the atmosphere which reduces its velocity. Hence the kinetic energy decreases, which is converted to heat energy. Potential energy is continuously decreasing, being converted to kinetic energy. There is also mass loss due to ablation.

Q4. Two bullets are fired at the same time with the same kinetic energy. If one bullet has twice the mass of the other, which has the greater speed and by what factor? Which can do most work?

Answer: The bullet that has less mass will have greater speed than the bullet of greater mass. It can be proved as follow;

Let mass of first bullet be m1 then the mass of the other bullet will be m₂= 2m₁.

Thus Thus it can be seen from the above equation that velocity v₁ of the bullet with mass m₁ is $\sqrt{2v_2}$ i.e. $\sqrt{2}$ times greater than the velocity v₂ of the bullet of mass m₂.

Since the kinetic energy of both the bullets is the same so, the work done by each of them will be equal.

Q5. Can an object have different amounts of gravitational potential energy if it remains at the same elevation?

Answer: No, an object can not have different amounts of gravitational potential energy as long as it stays on the earth. Gravitational potential energy is given by the formula;

Gravitational Potential Energy = mgh

As given the elevation remains the same it means ‘h’ is constant. The value of ‘g’ would be constant for the same elevation. Also the mass of the object is constant. Hence the gravitational potential energy remains the same. 

Q6. Why do roads leading to the top of a mountain wind back and forth?

Answer: Roads leading to the top of mountain wind back and forth because in this way less power is required is to move to the top than that of a single steep path.

According to the definition of power:

It is clear from the equation (i) that the greater the height, the greater would be the power required. If roads are made steeper, like in case of the inclined plane, the vertical height ‘h’ will be much larger due to this more power is required to reach to the top of mountains.

While for the roads that wind back and forth the steepness of the path is decreased by dividing it into the number of curved paths i.e. now the vertical height ‘h’ will be less for each path and so less power is required to reach to the top.

Q7. What type of energy conservation can be observed in water dams?

Answer: The stored water in dam’s possessing potential energy when these water are allowed to run turbines. The P.E of water converted to K.E when turbine runs the K.E is converted into mechanical energy. Turbines run generators which converts mechanical energy to electrical energy.

Q8. A meteor enters into earth’s atmosphere and burns. What happens to its kinetic energy?

Answer: When a meteor enters into earth’s atmosphere it burns and its K.E is converted into heat an light energy. And some is transferred to the K.E of air molecule.

Q9. What do you understand by term energy transformation support your answer by two examples?

Ans. Energy transformation is a process which converts energy from one form to another form it example are given.

1. When electrical energy is given to an electric motor it converts it to mechanical energy.

2. When fuel are burnt in an engine it converts fuel energy to mechanical energy.

Q10.  what kind of energy is possessed in the following cases? a) A stone laying on the top of a root b) Flying airplane. c) A wound up spring of a toy car.

Answer: a) A stone laying on the top of a root posses gravitational potential energy

 b) Flying airplane posses K.E energy due to motion and P.E due to its position.

c) A wound up spring of a boy car posses elastic P.E.

Descriptive Qs

Q1. Define energy? Also, give its different types?

Answer: Energy:- The ability of a body to do work is known as the energy it’s unit the same as work that is joules. Forms of energy:- different types of energy are given below.

(1)    Chemical energy:- Energy which is obtained during chemical reaction and burning of substances is called chemical energy e.g. burning of wood, coal and petroleum etc.

(2)    Nuclear energy:–That type of energy which is produced during a nuclear reaction is known as nuclear energy for an example process of nuclear fission.

(3)    Radicand energy:-The energy of electromagnetic waves is called radiant energy. For example radio waves microwaves x – rays etc have radiant energy.

(4)    Electrical energy:-That type of energy with the help of which we can operate different electrical equipment is called electrical energy.

(5)    Internal energy:–The energy of atoms and molecules which is usually in the formula kinetic energy and potential energy is called internal energy.

(6)    Mechanical energy:–The energy produced by moving parts of a machine is called mechanical energy.

(7)    Kinetic energy:–The energy produced in a body during motion is called kinetic energy.

(8)    Potential energy:–Energy possessed by a body by virtue of its position is called potential energy

(9)    Heat energy: –A form of energy which travels from one body to another due to the difference of their temperature is called heat energy.

(10)Sound energy:–The energy that gives the sensation of hearing is called sound energy.

Q2.  Which would have a greater effect on the K.E of an object doubling the mass or doubling the velocity?

Answer: K.E = $\frac{1}{2}{m v^2}$

When mass is doubled then energy increases two times

i.e., K.E' = $\frac{1}{2}{2m v^2}$

=> K.E' = 2($\frac{1}{2}{m v^2}$)

K.E' = 2 K.E

When velocity is doubled then energy increases 4 times

i.e., K.E' = $\frac{1}{2}{m (2v)^2}$

K.E' = $\frac{1}{2}{m 4v^2}$

K.E' = 4($\frac{1}{2}{m v^2}$)

=> K.E' = 4mv²

K.E' = 4 K.E

Q3. Define work and explain how work is calculated if force is applied at an angle.

Answer: Work: “Work is said to be done when a force acting on an object displaces it in the direction of force”.

Work is given by the formula;

Work = Force × displacement

W =F S

Work is a scalar quantity and its unit is joule (J)

1 J = 1 N.m

Calculation of work when force is applied at an angle:

Sometimes force and displacement do not have the same direction as shown in fig. Here the force ‘F’ is making an angle ‘θ’ with the displacement.

Resolving ‘F‘ into perpendicular components F_x and F_y as:

 F_x = Fcosθ

F_y = Fsinθ

In this case, only x-component of force i.e. F_x causes the body to move. Thus work done is only due to F_x and not F_y. Hence

W = F x S

W = (Fcosθ)S

W = FScosθ

Q4. Define kinetic energy. Derive the expression used for kinetic energy.

Answer: Kinetic energy: “The energy possessed by a body due to the virtue of its motion is called kinetic energy”.

It is denoted by “K.E ”. It is a scalar quantity

Derivation: Consider a situation in which all of the work done on the cart transfers only kinetic energy to the cart.

Consider a cart that is initially at rest. The cart moves the displacement ‘S‘ because of the horizontal force ‘F‘ applied to it. It achieves a final velocity of  v_f = v;

This work done ‘W’ appears as the kinetic energy KE such that

This equation shows the kinetic energy of a moving object with its mass and velocity . It demonstrate the work kinetic energy theorem which states that the work done on an object is equal to change in energy.

Q5. What is potential energy? Prove that the potential energy of a body of mass ‘m’ at a height ‘h’ above the surface of earth is given by mgh.

Answer: Potential energy: “The energy posses by a body due to the virtue of its position or configuration in a force field is called potential energy”. It is a scalar quantity and its SI unit is Joule.

Proof: Consider an object of mass ‘m’ being lifted vertically by a force ‘F’ to ‘h’ as shown in the figure.

The work done by the force F is given by the equation;

W = EG. Potential Energy = F x S  --- (i)

Since the force, in this case, is equal to its weight. So,

F = w = mg --- (ii)

Here the distance moved is the height ‘h’

Thus S = h --- (iii)

Putting equation (ii) and (iii) in equation (i), we get

EG. Potential Energy = mg x h

Q6. State the law of conservation of energy.

Answer: Law of Conservation of Energy: “Energy can neither be created nor destroyed in any process, It can be converted form one form to another, but total but only can be changed from one form to another form.”

Examples of the law of conservation of energy

1. The chemical energy stored in the food is converted into heat energy as a result of digestion in the body. This heat energy keeps our body warm and enables us to do the work.

2. In dams, the stored potential energy of water due to height is converted into kinetic energy to run the turbine for producing electrical energy.

Q7. Explain briefly major sources of energy. Such fossil fuels, wind, solar, biomass, nuclear and thermal energy.

Answer: Fossil Fuels: Fossil fuels are the remains of million-years-old plant life-now coal-or aquatic animal life-now gasoline and natural gas.

1. Coal: Coal is the most abundant fossil fuel in the world with an estimated reserve o one million metric tons. but burning coal results in significant atmospheric pollution.

2. Oil: Crude oil is refined into many different energy products such as gasoline, jet fuel, and heating oil. Despite the limited reserves of oil in the world, it is a preferred source over coal because oil produces more energy than the same amount of coal.

3. Natural gas: Natural gas is often a by-product of oil, it is a mixture of gases-the most common of which is methane. The advantage that natural gas has is that it is easy to transport. Fossil fuels are consumed in more than 80% of the world’s demand for energy. However, the waste gases produced in the consumption are polluting the atmosphere.

4. Wind Energy: The kinetic energy of the wind is currently used in many parts of the world to generate electricity. It is an eco-friendly source of energy but requires a very large open space.

5. Solar Energy: The energy from direct sunlight can be used to produce electricity. Today, solar cells are used to power everything from calculators and watches to small cities. It is very eco-friendly. However, a significant land area is required to produce a large amount of electricity.

6. Bio-mass: Bio means “life” and bioenergy is the energy from living things. The term biomass refers to the material from which we get bioenergy. Biomass is produced when the sun’s solar energy is converted into plant matter(carbohydrates) by the process of photosynthesis.

7. Nuclear Energy: Nuclear energy is the energy obtained from nuclear fission reactions. When extremely large atoms split into two or more pieces, an enormous amount of energy is released in the form of radiation or heat. The heat is used to boil water that is eventually used to generate electricity.

8. Thermal Energy: Thermal energy is the energy recovered from the Earth’s core. The thermal energy contained within the Earth’s core results from the energy trapped almost five billion years ago during the formation of the planet. This energy is used to generate electricity.

Q8. Define and explain power?

Answer: Power: “The time rate of doing work is known as power.” It measures how fast work is done or how fast energy is being converted from one form to another form. Like work, power is a scalar quantity.

Mathematical Expression: Mathematically, it can also be defined as the ratio of work and time.

Unit: The S.I unit of power is the watt (W) which is defined as: “The power of an object is 1 watt if it does work at the rate of one joule per sec”

In the British system, the unit of power is the foot-pound per second (ft.lb/s). However, for practical purposes, a large unit is often used which is horsepower (hp).

1 hp = 746 W = 550 ft.lb/s

Explanation: Power not only explains how much work is done on the body in order to displace it through some distance or to some height but it also gives information about how much time is required in doing that work. Thus unlike work, it makes a reference to the passage of time, too i.e. it also describes how quickly the work is done on the object or system.

Numerical Problems

1 A man has pulled a cart through 35m applying a force of 300N. Find the work done by the man.

Given Data: Force = F = 300N      Distance = d= 35m

To find: Work = W = ?

Solution: W = F.S = 300 x 35

⇒ W = 10500J ANS

2 A block weighing 20N is lifted 6m vertically upward. Calculate the potential energy stored in it.

Given Data: Weight = w = mg = 20N        h = 6m

To find: Potential Energy = ?

Solution: P.E = mgh = wh P.E = 20 X 6

⇒ P.E 120J ANS

3 A car weighing 12kN has a speed of 20ms^-1. Find its kinetic energy.

Given Data: W = mg = 12kN = 12000N m =  = 1200kg    v = 20ms^-1

To find: K.E = ?

Solution: K.E = $\frac{1}{2}$mv² = $\frac{1}{2}$(1200)(20)²

K.E = 240,000J = 240kJ ANS

4 A 500g stone is thrown up with a velocity of 15ms^-1. Find its (i) P.E. at its maximum height.(ii) K.E. when it hits the ground.

Given Data: m = 500g = 0.5kg      v = 15ms^-1

To find: K.E =?   P.E =?

Solution: K.E = $\frac{1}{2}$mv² = $\frac{1}{2}$(0.5)(15)² = $\frac{1}{2}$(0.5)(225)

K.E = 56.25J ANS

For upward movement: v_i = 15ms^-1         v_f = 0ms^-1

g = -10ms^-2          h =?

2gh =  v_f² - v_i²

⇒ h = $\frac{v_f^2 - v_i^2}{2g}$

h = $\frac{0^2 - 15^2}{2(-10)} = \frac{0 - 225}{-20} = \frac{-225}{-20}$

⇒ h = 11.25m

P.E = mgh = 0.5 × 10 × 11.25

⇒ P.E = 56.25J ANS

Total amount of energy remains constant.

5 On reaching the top of a slope 6m high from its bottom a cyclist has a speed of 1.5ms^-1. Find the kinetic energy and the potential energy of the cyclist. The mass of the cyclist and his bicycle is 40kg.

Given Data: v = 1.5 ms^-1    m = 40kg          h = 6m

To find: K.E =?   P.E =?

Solution: K.E = K.E = $\frac{1}{2}$mv² = $\frac{1}{2}$(40)(1.5)² = $\frac{1}{2}$(40)(2.25)

⇒ K.E = 45J ANS

P.E = mgh = 40 x 10 x 6

⇒ P.E = 2400J ANS

6 A motor boat moves at a steady speed of 4ms^-1. Water resistance acting on it is 4000N. Calculate the power of its engine.

Given Data: F = 4000N   v = 4ms^-1

To find: P =?

Solution: P = $\frac{W}{t} = \frac{FS}{t}$  As (W=FS)

P = Fv   As (v=S/t)

P = 4000 x 4

⇒ P = 16000W = 16kW ANS

7 A man pulls a block with a force of 300N through 50m in 60s. Find the power used by him to pull the block.

Given Data: F = 300N        S = 50m        t = 60s 

To find: Power = P =?

Solution: P = $\frac{W}{t} = \frac{FS}{t}$  As (W=FS)

P $\frac{300 × 50}{60} = \frac{15000}{60}$

⇒ P = 250W ANS

8 A 50kg man moved 25 steps up in 20 seconds. Find the power, if each step is 16cm high.

Given Data:  m = 50kg      Steps =25            t =20s Height of one step = 16cm = 0.16m Height of 25 steps = 0.16 × 25 = 4m

To find: P =?

Solution: P = $\frac{W}{t} = \frac{FS}{t} = \frac{mgh}{t}$  As (W=FS) & (F = w = mg)

P $\frac{50 × 10 × 4}{20} = \frac{2000}{20}$

P = 100Watts ANS

9 Calculate the power of a pump which can lift 200kg of water through a height of 6m is 10 seconds.

Given Data:  m= 200kg        t = 10s             h = 6m

To find: P =?

Solution: P = $\frac{W}{t} = \frac{FS}{t} = \frac{mgh}{t}$  As (W=FS) & (F = w = mg)

P $\frac{200 × 10 × 6}{10} = \frac{12000}{10}$

P = 1200Watts ANS

10 An electric motor of 1hp is used to run water pump. The water pump takes 10 minutes of fill an overhead tank. The tank has a capacity of 800 liters and height of 15m. Find the actual work done by the electric motor to fill the tank. Also find the efficiency of the system. (Density of water = 1000kgm^-3) (Mass of 1 liter of water = 1kg)

Given Data: Input Power of motor = 1hp = 746W

Time taken = t = 10m = 600s

Height = h = 15m

Density of water = ρ = 1000kgm^-3

Mass of 1 liter of water = 1kg

To find: Input work = W_i =?         %Efficiency =?

Solution: P_i = $\frac{W_i}{t}$

⇒ W_i = P_i x t = 746 × 600

W_i = 447600J ANS

Mass of 800l water = m = 800kg

Output Work= P.E = mgh = 800 × 10 × 15

⇒ P.E = 120000J

%Efficiency = $\frac{Output}{Input}$ × 100%

%Efficiency = $\frac{120000}{447600}$ × 100%

%Efficiency =26.8% ANS