WORK,POWER,ENERGY

CHAPTER :- WORK,POWER,ENERGY

(SECTION-A)

1. A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle

(A) (B) Zero

2. A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by , where x is in metres and t is in seconds. The work done during the first 4 seconds is

(A) 5.28 J (B) 450 Mj

3. A particle is dropped from a height h. A constant horizontal velocity is given to the particle. Taking g to be constant every where, kinetic energy E of the particle with respect to time t is correctly shown in

(A)

(B)

(C)

(D)

4. A force acting on a particle causes a displacement: in its own direction. If the work done is then the value of is

(A) 0 (B) 1 (C) 6 (D) 12

5. A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that

(A) Its velocity is constant

(B) Its acceleration is constant

(D) It moves in a straight line

6. A particle moves under the effect of a force F = Cx from x = 0 to . The work done in the process is

(A) (B)

7. The potential energy of a certain spring when stretched through a distance ‘S’ is 10 joule. The amount of work (in joule) that must be done on this spring to stretch it through an additional distance ‘S’ will be

(A) 30 (B) 40 (C) 10 (D) 20

8. The spring extends by x on loading, then energy stored by the spring is :

(if T is the tension in spring and k is spring constant)

(A) (B)

9. The potential energy between two atoms in a molecule is given by ; where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium when

(A) (B)

10. A light and a heavy body have equal momenta. Which one has greater K.E

(A) The light body

(B) The heavy body

(D) Data is incomplete

11. A body of mass 2 kg is thrown up vertically with K.E. of 490 joules. If the acceleration due to gravity is 9.8, then the height at which the K.E. of the body becomes half its original value is given by

(A) 50 m (B) 12.5 m

12. If the K.E. of a body is increased by 300%, its momentum will increase by

(A) 100% (B) 150%

13. A light and a heavy body have equal kinetic energy. Which one has a greater momentum ?

(A) The light body

(B) The heavy body

(D) It is not possible to say anything without additional information

14. A 4 kg mass and a 1 kg mass are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is

(A) 1 : 2 (B) 1 : 1

15. A block of mass m is attached to two unstretched springs of spring constants k1 and k2 as shown in figure. The block is displaced towards right through a distance x and is released. Find the speed of the block as it passes through the mean position shown.

(A) (B)

16. What is the velocity of the bob of a simple pendulum at its mean position, if it is able to rise to vertical height of (Take

(A) 0.6 m/s (B) 1.4 m/s

17. A bomb of mass 9kg explodes into 2 pieces of mass 3kg and 6kg. The velocity of mass 3kg is 1.6 m/s, the K.E. of mass 6kg is.

(A) 3.84 J (B) 9.6 J

18. A bomb of mass 3.0 Kg explodes in air into two pieces of masses 2.0 kg and 1.0 kg. The smaller mass goes at a speed of 80 m/s.The total energy imparted to the two fragments is.

(A) 1.07 kJ (B) 2.14 kJ

19. A block of mass m initially at rest is dropped from a height h on to a spring of force constant k. the maximum compression in the spring is x then.

(A)

(B)

(C)

(D)

20. A body of mass m accelerates uniformly from rest to in time . As a function of time t, the instantaneous power delivered to the body is.

(A) (B)

21. A weight lifter lifts 300 kg from the ground to a height of 2 meter in 3 second. The average power generated by him is

(A) 5880 watt (B) 4410 watt

22. A 60 kg man runs up a staircase in 12 seconds while a 50 kg man runs up the same staircase in 11, seconds, the ratio of the rate of doing their work is

(A) 6 : 5 (B) 12 : 11

23. A force of acts on a body for 4 second, produces a displacement of The power used is

(A) 9.5 W (B) 7.5 W

24. A wedge of mass M fitted with a spring of stiffness ‘k’ is kept on a smooth horizontal surface. A rod of mass m is kept on the wedge as shown in the figure. System is in equilibrium. Assuming that all surfaces are smooth, the potential energy stored in the spring is :

(A) (B)

25. A car of mass ‘m’ is driven with acceleration ‘a’ along a straight level road against a constant external resistive force ‘R’. When the velocity of the car is ‘V’, the rate at which the engine of the car is doing work will be

(A) RV (B) maV

26. A particle of mass m moving with horizontal speed 6 m/sec as shown in figure. If then for one dimensional elastic collision, the speed of lighter particle after collision will be

(A) 2m/sec in original direction

(B) 2 m/sec opposite to the original direction

(D) 4 m/sec in original direction

27. A steel ball of radius 2 cm is at rest on a frictionless surface. Another ball of radius 4cm moving at a velocity of 81 cm/sec collides elastically with first ball. After collision the smaller ball moves with speed of

(A) 81 cm/sec (B) 63 cm/sec

28. A particle moves under the influence of a force F = kx in one dimensions (k is a positive constant and x is the distance of the particle from the origin). Assume that the potential energy of the particle at the origin is zero, the schematic diagram of the potential energy U as a function of x is given by

(A)

(B)

(C)

(D)

29. Which of the following statements is true

(A) In elastic collisions, the momentum is conserved but not in inelastic collisions

(B) Both kinetic energy and momentum are conserved in elastic as well as inelastic collisions

(D) Total kinetic energy is conserved in elastic collisions but momentum is not conserved in elastic collisions

30. A mass 'm' moves with a velocity 'v' and collides inelastically with another identical mass. After collision the Ist mass moves with velocity in a direction perpendicular to the initial direction of motion. Find the speed of the 2^nd mass after collision

(A) (B)

31. A bullet hits and gets embedded in a solid block resting on a horizontal frictionless table. What is conserved ?

(A) Momentum and kinetic energy

(B) Kinetic energy alone

(D) Neither momentum nor kinetic energy

32. A moving body of mass m and velocity 3 km/h collides with a rest body of mass 2m and sticks to it. Now the combined mass starts to move. What will be the combined velocity

(A) 3 km/h (B) 2 km/h

33. A metal ball of mass 2 kg moving with a velocity of 36 km/h has an head on collision with a stationary ball of mass 3 kg. If after the collision, the two balls move together, the loss in kinetic energy due to collision is

(A) 40 J (B) 60 J

34. A force-time graph for a linear motion is shown in figure where the segments are circular. The linear momentum gained between zero and 8 second is

(A)

(B)

(C)

(D)

35. Figure shows the F-x graph. Where F is the force applied and x is the distance covered

by the body along a straight line path. Given that F is in newton and x in metre, what is the work done ?

(A) 10 J (B) 20 J

(SECTION-B)

36. Assertion : The rate of change of total momentum of a many particle system is proportional to the sum of the internal forces of the system.

Reason : Internal forces can change the kinetic energy but not the momentum of the system.

(A) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(B) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(D) Both assertion and reason are false

37. A body of mass 6kg is under a force which causes displacement in it given by metres where t is time. The work done by the force in 2 seconds is

(A) 12 J (B) 9 J

38. If W1, W2 and W3 represent the work done in moving a particle from A to B along three different paths 1, 2, 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W1, W2 and W3

(A) W1 > W2 > W3

(B) W1 = W2 = W3

(D) W2 > W1 > W3

39. A uniform chain of length 2m is kept on a table such that a length of 60cm hangs freely from the edge of the table. The total mass of the chain is 4kg. What is the work done in pulling the entire chain on the table

(A) 7.2 J (B) 3.6 J

40. An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 m/s. The mass per unit length of water in the pipe is 100 kg/m. What is the power of the engine?

(A) 400 W (B) 200 W

41. The force constant of a wire is k and that of another wire is When both the wires are stretched through same distance, then the work done

(A) (B)

42. A mass of 0.5kg moving with a speed of 1.5 m/s on a horizontal smooth surface, collides with a nearly weightless spring of force constant . The maximum compression of the spring would be

(A) 0.15 m (B) 0.12 m

43. A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P0. The instantaneous velocity of this car is proportional to :

(A) t2P0 (B) t1/2

44. Power of a water pump is 2 kW. If , the amount of water it can raise in one minute to a height of 10 m is

(A) 2000 litre (B) 1000 litre

45. How much work does a pulling force of 40 N do on the 20 kg box in pulling it 8 m across the floor at a constant speed. The pulling force is directed at 60° above the horizontal

(A) 160 J

(B) 277 J

(D) None of the above

46. Work done in time t on a body of mass m which is accelerated from rest to a speed v in time as a function of time t is given by

(A) (B)

47. The slope of kinetic energy displacement curve of a particle in motion is

(A) Equal to the acceleration of the particle

(B) Inversely proportional to the acceleration

(D) None of the above

48. The energy required to accelerate a car from 10 m/s to 20 m/s is how many times the energy required to accelerate the car from rest to 10 m/s

(A) Equal (B) 4 times

49. A body of mass 2 kg slides down a curved track which is quadrant of a circle of radius 1 metre. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is

(A) 4.43 m/sec (B) 2 m/sec

50. Match the column I with column II.

Column I

(i) When a body does work against friction, its kinetic energy

(ii) Work done by a body is

(iii) Power of a body varies inversely as

(iv) When work done over a closed path is zero

Column II

(p) independent of time

(q) time

(r) force must be conservative

(s) decreases

(A) i-p,ii-q, iii-r,iv-s

(B) i-q,ii-r, iii-s,iv-p

(D) i-s,ii-p, iii-q,iv-r

CHAPTER :- WORK,POWER,ENERGY

ANSWER KEY

1. (B) 2. (A) 3. (A) 4. (C) 5. (C) 6. (B) 7. (A)

8. (A) 9. (D) 10. (A) 11. (B) 12. (A) 13. (B) 14. (C)

15. (A) 16. (B) 17. (C) 18. (D) 19. (B) 20. (D) 21. (D)

22. (C) 23. (A) 24. (C) 25. (C) 26. (A) 27. (C) 28. (A)

29. (C) 30. (A) 31. (C) 32. (C) 33. (B) 34. (B) 35. (A)

36. (D) 37. (D) 38. (B) 39. (B) 40. (A) 41. (B) 42. (A)

43. (B) 44. (D) 45. (A) 46. (D) 47. (C) 48. (D) 49. (A)

50. (D)

SOLUTIONS

SECTION-A

1. (B)

Sol. Work done by centripetal force is always zero, because force and instantaneous displacement are always perpendicular.

2. (A)

Sol.

\ and

(According to work energy theorem)

3. (A)

Sol. h = gt2, W = mgh = mg , W = Kf – Ki

= Kf – mu2, Kf = mu2 +

Hence Ans. is (A)

4. (C)

Sol.

5. (C)

Sol. When a force of constant magnitude which is perpendicular to the velocity of particle acts on a particle, work done is zero and hence change in kinetic energy is zero.

6. (B)

Sol.

7. (A)

Sol. (given in the problem)

= 3 × 10 = 30 J

8. (A)

Sol.

9. (D)

Sol. Condition for stable equilibrium

Þ Þ

Þ Þ Þ

10. (A)

Sol. if P = constant then

11. (B)

Sol. Let h is that height at which the kinetic energy of the body becomes half its original value i.e. half of its kinetic energy will convert into potential energy

\ mgh = Þ Þ

12. (A)

Sol. Let initial kinetic energy,

Final kinetic energy, of E = 4E

As ÞÞ

Þ of

i.e. Momentum will increase by 100%

13. (B)

Sol. if E are equal then

i.e. heavier body will possess greater momentum.

14. (C)

Sol. If E are const. then = 2

15. (A)

Sol. K2 x2 + K1x2 = m v2

v =

16. (B)

Sol.

17. (C)

Sol.

As the bomb initially was at rest therefore

Initial momentum of bomb = 0

Final momentum of system =

As there is no external force

\ Þ

velocity of 6 kg mass (numerically)

Its kinetic energy

18. (D)

Sol. Both fragment will possess the equal linear momentum

Þ Þ

\ Total energy of system

= 4800 J = 4.8 kJ

19. (B)

Sol. Change in gravitational potential energy

= Elastic potential energy stored in compressed spring

20. (D)

Sol. [as u = 0]

21. (D)

Sol. P=

22. (C)

Sol. Þ (As h = constant)

23. (A)

Sol.

24. (C)

Sol. For m, N cos q = mg

For M , N sin q = kx

So tan q =

so Kx2 =

25. (C)

Sol. F – R = ma, F = R + ma,

P = Fv = (R + ma)v

26. (A)

Sol.

Substituting m₁ = 0,

i.e. the lighter particle will move in original direction with the speed of 2 m/s.

27. (C)

Sol. Ratio in radius of steel balls = 1/2

So, ratio in their masses [As]

Let and

28. (A)

Sol. From F =

\ U(x) =

as U(0) = 0

Therefore, the correct option is (A).

29. (C)

30. (A)

Sol. Let mass A moves with velocity v and collides inelastically with mass B, which is at rest.

According to problem mass A moves in a perpendicular direction and let the mass B moves at angle q with the horizontal with velocity v.

Initial horizontal momentum of system

(beforecollision)=mv ....(i)

Final horizontal momentum of system

(after collision) = Mv cosq ...(ii)

From the conservation of horizontal linear momentum mv = mV cosq Þ v = V cosq ...(iii)

Initial vertical momentum of system (before collision) is zero.

Final vertical momentum of system

From the conservation of vertical linear momentum

Þ ...(iv)

By solving (iii) and (iv)

Þ Þ .

31. (C)

32. (C)

Sol.

Initial momentum =

Final momentum =

By the law of conservation of momentum

33. (B)

Sol.

By law of conservation of momentum

Loss in K.E.

34. (B)

Sol. Here \ K.E.

Total energy

35. (A)

Sol. Work done = area under curve and displacement axis

SECTION-B

36. (D)

Sol. Rate of change of momentum is proportional to external forces acting on the system. The total momentum of whole system remain constant when no external force is acted upon it.

Internal forces can change the kinetic energy of the system.

37. (D)

Sol. (D) \