Q: Question 9A truck of mass 1000 kg increases its speed from 36 km h-1 to 72 km h-1. Find the increase in its kinetic energy.

Given:Mass (m) = 1000 kg1 km h-1 = 518\dfrac{\text{5}}{\text{18}}185 m s-136 km h-1 = 518\dfrac{\text{5}}{\text{18}}185 x 36 = 10 m s-1So, initial speed (v1) = 10 m s-11 km h-1 = 518\dfrac{\text{5}}{\text{18}}185 m s-172 km h-1 = 518\dfrac{\text{5}}{\text{18}}185 x 72 = 20 m s-1So, final speed (v2) = 72 km h-1 = 20 m s-1Increase in its kinetic energy = ?Increase in kinetic energy = 12\dfrac{\text{1}}{\text{2}}21 m[(v2)2 - (v1)2]= 12\dfrac{\text{1}}{\text{2}}21 x 1000 x [(20)2 - (10)2]= 500 x [400 - 100]= 500 x 300= 150000 J or 1.5 x 105 JSo increase in kinetic energy = 1.5 x 105 J.

Question 1

Question 2(b)Assertion (A) : When a ball is dropped from a height, its kinetic energy decreases and potential energy increases.Reason (R) : The total mechanical energy remains conserved during the fall, if we ignore air resistance.Both A and R are true and R is the correct explanation of ABoth A and R are true and R is not the correct explanation of AAssertion is true but reason is falseAssertion is false but reason is true

Accepted Answer

Assertion is false but reason is trueExplanationAssertion (A) is false because when the ball is released from a height, it falls down and the vertical height of the ball from the ground decreases. Therefore, the potential energy decreases and it changes to kinetic energy due to which the speed of ball increases.Reason (R) is true because during the fall while transformation of mechanical energy from one form to the other desired form, some part of it changes to other undesirable form usually heat due to the presence of air resistance but when air resistance is absent then no losses occur and hence the total mechanical energy remains conserved.

Question 2

Question 3Fill in the blanks:(a) Work is said to be done by a force only when ............... .(b) Work done = Force x ............... .(c) The energy of a body is its capacity to do ............... .(d) The S.I. unit of energy is ............... .(e) The potential energy of a body is due to its ............... and kinetic energy of a body is due to its ............... .(f) Gravitational potential energy U = mass x force of gravity on unit mass x ............... .(g) Kinetic energy = 12\dfrac{	ext{1}}{	ext{2}}21​ x mass x ............... .(h) Power P = ............... / time taken.(i) The S.I. unit of power is ............... .(j) 1 H.P. = ............... W.

Accepted Answer

(a) Work is said to be done by a force only when the body moves.(b) Work done = Force x distance moved in the direction of force.(c) The energy of a body is its capacity to do work.(d) The S.I. unit of energy is joule .(e) The potential energy of a body is due to its state of rest or position and kinetic energy of a body is due to its state of motion.(f) Gravitational potential energy U = mass x force of gravity on unit mass x vertical height.(g) Kinetic energy = 12\dfrac{	ext{1}}{	ext{2}}21​ x mass x (speed)2.(h) Power P = Work done by the body / time taken.(i) The S.I. unit of power is watt (W).(j) 1 H.P. = 746 W.

Question 3

Question 5Give an example to show the conversion of potential energy to kinetic energy when put in use.

Accepted Answer

Consider a ball placed at a height. It will have only potential energy and no kinetic energy.If the ball is released from the height, it falls down and the vertical height of the ball from the ground decreases. Therefore, the potential energy decreases and it changes to kinetic energy due to which the speed of the ball increases. During the fall, the ball has both the potential energy and the kinetic energy. As the ball reaches the ground, the potential energy becomes zero and it changes entirely into kinetic energy.The below figure shows the conversion of potential energy into kinetic energy during the vertical free fall of a ball at various positions A, B and C.

Question 4

Question 4Two bodies of same masses are placed at height h and 2h. Compare their gravitational potential energy.

Accepted Answer

Given:Mass of first body = Mass of second body = mHeight of first body = hHeight of second body = 2hg is same for both the bodies.We know Gravitational potential energy = mghGravitation potential energy of first body (U1) = mghGravitation potential energy of second body (U2)= mg2h = 2mghOn comparing both gravitational potential energy:U1U2=mgh2mgh=12\dfrac{	ext{U}_1}{	ext{U}_2} = \dfrac{	ext{mgh}}{	ext{2mgh}} = \dfrac{	ext{1}}{	ext{2}}U2​U1​​=2mghmgh​=21​So, gravitational potential energy of first body : gravitational potential energy of second body = 1 : 2.

Question 5

Question 6The gravitational potential energy stored in a box of weight 150 kgf is 1.5 x 104 J. Find the height of the box. Take 1 kgf = 10 N.

Accepted Answer

Given:Gravitational potential energy (U) = 1.5 x 104 J = 15000 JWeight = 150 kgf = 150 x 10 = 1500 Nheight h = ?U = mgh15000 = 1500 x hh = 150001500\dfrac{	ext{15000}}{	ext{1500}}150015000​h = 10 mSo height of the box = 10 m.

Question 6

Question 7The potential energy of a body of mass 0.5 kg increases by 100 J when it is taken to the top of a tower from the ground. If the force of gravity on 1 kg = 10 N, what is the height of the tower?

Accepted Answer

Given:Potential energy (U) = 100 JMass (m) = 0.5 kgForce of gravity on 1 kg mass = 10 Nheight (h) = ?U = mgh100 = 0.5 x 10 x hh = 1005\dfrac{	ext{100}}{	ext{5}}5100​h = 20 mSo height of the tower = 20 m.

Question 7

Question 8A body of mass 60 kg is moving with a speed 50 m s-1. Find its kinetic energy.

Accepted Answer

Given:Mass (m) = 60 kgSpeed (v) = 50 m s-1Kinetic energy = ?Kinetic energy = 12\dfrac{	ext{1}}{	ext{2}}21​ x mv2= 12\dfrac{	ext{1}}{	ext{2}}21​ x 60 x (50)2= 30 x 2500= 75000 J or 7.5 x 104 JSo kinetic energy = 7.5 x 104 J.

Question 8

Question 9A truck of mass 1000 kg increases its speed from 36 km h-1 to 72 km h-1. Find the increase in its kinetic energy.

Accepted Answer

Given:Mass (m) = 1000 kg1 km h-1 = 518\dfrac{	ext{5}}{	ext{18}}185​ m s-136 km h-1 = 518\dfrac{	ext{5}}{	ext{18}}185​ x 36 = 10 m s-1So, initial speed (v1) = 10 m s-11 km h-1 = 518\dfrac{	ext{5}}{	ext{18}}185​ m s-172 km h-1 = 518\dfrac{	ext{5}}{	ext{18}}185​ x 72 = 20 m s-1So, final speed (v2) = 72 km h-1 = 20 m s-1Increase in its kinetic energy = ?Increase in kinetic energy = 12\dfrac{	ext{1}}{	ext{2}}21​ m[(v2)2 - (v1)2]= 12\dfrac{	ext{1}}{	ext{2}}21​ x 1000 x [(20)2 - (10)2]= 500 x [400 - 100]= 500 x 300= 150000 J or 1.5 x 105 JSo increase in kinetic energy = 1.5 x 105 J.

Question 9

Question 10A car is moving with a speed of 15 km h-1 and another identical car is moving with a speed of 30 km h-1. Compare their kinetic energy.

Accepted Answer

Speed of first car = 15 km h-1Speed of second car = 30 km h-1Mass of both cars = mKinetic energy of first car (K1) = 12\dfrac{	ext{1}}{	ext{2}}21​ x mv2= 12\dfrac{	ext{1}}{	ext{2}}21​ x m x (15)2= 2252\dfrac{	ext{225}}{	ext{2}}2225​ x m= 112.5 m JKinetic energy of second car (K2) = 12\dfrac{	ext{1}}{	ext{2}}21​ x mv2= 12\dfrac{	ext{1}}{	ext{2}}21​ x m x (30)2= 9002\dfrac{	ext{900}}{	ext{2}}2900​ x m= 450 m JComparing the kinetic energy we get:K1K2=112.5 m450 m=14\dfrac{	ext{K}_1}{	ext{K}_2} = \dfrac{	ext{112.5 m}}{	ext{450 m}} = \dfrac{	ext{1}}{	ext{4}}K2​K1​​=450 m112.5 m​=41​So Kinetic energy of first car (K1) : Kinetic energy of second car (K2) = 1 : 4.

Question 10

Question 11A pump raises water by spending 4 x 105 J of energy in 10 s. Find the power of pump.

Accepted Answer

Given:Work done by pump = Energy spent = 4 x 105 J or 400000 Jtime = 10 sPower = ?Power = Work donetime taken\dfrac{	ext{Work done}}{	ext{time taken}}time takenWork done​= 40000010\dfrac{	ext{400000}}{	ext{10}}10400000​= 40000 W or 4 x 104 WSo power spent by the pump = 4 x 104 W.

Question 11

Question 12It takes 20 s for a girl A to climb up the stairs while girl B takes 15 s for the same job. Compare:(a) The work done and(b) The power spent by them.

Accepted Answer

(a) Both the girls move the same distance and force is also equal on both. Hence, the work done by both the girls is the same.∴ Work done by girl A : Work done by girl B = 1 : 1(b) Power spent = Work donetime taken\dfrac{\text{Work done}}{\text{time taken}}time takenWork done​We know,Work done by girl A = Work done by girl B = WPower spent by girl A (PA) = W20\dfrac{\text{W}}{\text{20}}20W​Power spent by girl B (PB) = W15\dfrac{\text{W}}{\text{15}}15W​Comparing the power spent by girl A and girl B:PAPB=W20W15=1520=34\dfrac{\text{P} _\text{A}}{\text{P} _\text{B}} = \dfrac{\dfrac{\text{W}}{\text{20}}}{\dfrac{\text{W}}{\text{15}}} \[1em] = \dfrac{\text{15}}{\text{20}} = \dfrac{\text{3}}{\text{4}}PB​PA​​=15W​20W​​=2015​=43​∴ Power spent by girl A : Power spent by girl B = 3:4.

Question 12

Question 1(c)Two coolies A and B do some work in time 1 minute and 2 minute respectively. The power spent is:same by both cooliesis more by coolie A than by Bis less by coolie A than by Bnothing can be said

Accepted Answer

is more by coolie A than by BReason — Power spent = Work donetime taken\dfrac{	ext{Work done}}{	ext{time taken}}time takenWork done​.Since coolie A takes less time than coolie B so power spent by coolie A is more than coolie B.

Question 13

Question 13What is potential energy? State its unit.

Accepted Answer

Potential energy of a body is the energy possessed by it due to its state of rest or position. Its unit is joule (J).

Question 14

Question 14Give one example of a body that has potential energy, in each of the following:(a) due to its position at a height,(b) due to its elongated stretched state.

Accepted Answer

(a) A stone placed at a height has potential energy because of its position. It is known as gravitational potential energy.(b) A stretched rubber band has potential energy due to its elongated stretched state. It is known as elastic potential energy.

Question 15

Question 15A bucket full of water is on the first floor of your house and another identical bucket with same quantity of water is kept on the second floor. Which of the two has greater potential energy?

Accepted Answer

The bucket kept on second floor has greater potential energy.Reason — The two buckets are identical containing the same amount of water so their mass is same. Value of g is also same for the two buckets. As the bucket on second floor is at a greater height hence its potential energy is also greater.

Question 16

Question 16Write the expression for the gravitational potential energy explaining the meaning of the symbols used?

Accepted Answer

Gravitational potential energy (U) = mghwhere,m is mass of the body,g is acceleration due to gravity andh is height of the body above ground level.

Question 17

Question 17Define the term kinetic energy. Give one example of a body which possess kinetic energy.

Accepted Answer

Kinetic energy of a body is the energy possessed by it due to its state of motion. Example: A fast moving stone has kinetic energy which has the capacity of breaking a window pane.

Question 18

Question 18State two factors on which the kinetic energy of a moving body depends.

Accepted Answer

The two factors on which the kinetic energy of a moving body depends are:The mass of the body — Greater the mass of the body, higher is its kinetic energy.The speed of the body — More the speed of the body, higher is its kinetic energy.

Question 19

Question 19Two toy cars A and B of masses 200 g and 500 g respectively are moving with the same speed. Which of the two has greater kinetic energy?

Accepted Answer

The toy car B has greater kinetic energy than toy car A.Reason — The two toy cars A and B are moving with the same speed. As the toy car B has greater mass (500 g) than toy car A (200 g) hence its kinetic energy is also greater.

Question 20

Question 20A cyclist doubles his speed. How will his kinetic energy change: increase, decrease or remain the same?

Accepted Answer

Kinetic energy of cyclist will increase as speed is doubled because more the speed of the body, more is its kinetic energy.

Energy

Exercise 4 Assertion Reason Type

Exercise 4 Fill In The Blanks

Exercise 4 Long Answer Type Questions

Exercise 4 Numericals

Exercise 4 Objective Type Questions

Exercise 4 Short Answer Type Questions