PRCTICE SHEET WPE

1. A block of mass m moves on a vertical track which is convex at A and concave at B as shown in figure. If the friction is assumed to be negligible, find the ratio of the normal reactions at A and B. Velocity at the highest point is v0 and radius of curvature at A and B are equal to R.

2 AOB is a smooth semicircular track of radius r. A block of mass m

is given a velocity parallel to track at point A. Calculate normal reaction between block and track when block reaches at point O.

3. A body of mass m dropped from a certain height strikes a light vertical fixed spring of stiffness k. Find the height of its fall before touching the spring if the maximum compression of the spring is equal to 3mg/k.

4. An ideal massless spring 's' can be compressed 1.0 m by a 100 N force. It is placed as shown at the bottom of a frictionless inclined plane which makes an angle of q = 300 with the horizontal. A 10 kg block is released from rest from the top of the incline and is brought to rest momentarily after compressing the spring 2.0 m. Through what distance does the mass slide before coming to rest ?

5. A block of mass m is attached to two unstretched springs of spring constant 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 a distance x/4 from its mean position.

6 A body of mass 1kg is projected with a velocity v = 5 m/s from the surface of earth at an angle of q = 600 with the horizontal. What is the power developed by the gravitational force at the following instants (a) At point M (highest point)(b) At point N

7. A bob of mass 'm' is suspended by a light inextensible string of length 'l' from a fixed point. The bob is given a speed of . Find

the tension in the string when string deflects through an angle 1200 from the vertical.

8. Consider the arrangement shown in the figure. If the system is set free at t = 0 with the horizontal bar at a height of h as shown in the figure, obtain

(i) velocities of the wedges A and B at the instant C hits the floor.(ii) Force exerted by the bar C on each of the wedge.(Neglect any friction. Mass of each wedge is m while that of C is M)

9. A train starting from rest is moving along a straight track with a constant acceleration of 2.5 m/s2. A passenger at rest in the train observes a particle of mass 2 kg to be at rest on the floor with which it has a coefficient of friction ms = mk = 0.5. Six seconds after the starting of the train, a horizontal force F = 13 N is applied to the particle for two seconds duration. The passenger now observes the particle to move perpendicular to the direction of the train. (a) calculate the kinetic energy of the particle with respect to the passenger at the end of 8 seconds after starting of the train.(b) repeat the calculation of (a) for an observer on the ground.

10. A small ball B, of mass MB, is suspended through a massless rigid rod of length l and is attached to plank A of mass mA. The plank is free to slide on a frictionless horizontal track. If the ball is given an initial horizontal velocity v o

when the plank was at rest, determine, (a) the velocity of ball B as it reached its maximum elevation,(b) the maximum vertical distance h through which B will rise

11 A particle is suspended vertically from a point O by an inextensible massless string of length 'L'. A vertical line AB is at a distance L/8 from O as is shown. A horizontal velocity 'u' is imparted to the particle. At horizontal velocity 'u' is imparted to the particle. At some point its motion ceases to be circular and eventually the object passes through line AB. At the instant of crossing AN, its velocity is horizontal. Find out the value of 'u'.

12. A body starts moving from the highest point of the smooth curved surface horizontal at the end as shown in figure without losing contact. Find out the horizontal distance moved by the body after breaking off at point P from the curved surface.

13. A small disc of mass m slides down a smooth hill of height h without initial velocity and gets onto a planck of mass M lying on the horizontal plane at the base of the hill, as shown in the figure. Due to friction between the disc and the plank, the disc slows down and ultimately, both move together.

(a) Find the common velocity of the disc and the planck.(b) Find the work done by the friction(c) Find the distance moved by the disc with respect to the planck before they start moving together.

14. A block of mass 'm' is pushed against a spring of spring constant k fixed at other end to a wall. The block can slide on a frictionless table as shown. The natural length of the spring is L0. It is compressed to half its natural length and released. Find the velocity of the block as a function of its distance from the wall.

15. An object of mass 5 kg falls from rest through a vertical distance of 20 m and reaches a velocity of 10 m/s. How much work is done by the push of the air on the object?

16. Two masses ‘m’ and ‘2m’ are connected by a massless string which passes over a light frictionless pulley as shown in fig.1. The masses are initially held with equal lengths of the strings on either side of the pulley. Find the velocity of the masses at the instant the lighter mass moves up a distance of 6.54 m. The string is suddenly cut at that instant. Calculate the time taken by each to reach the ground. (g = 9.81 m/s2)

1. A particle of mass m is projected with velocity u at an angle q with horizontal . During the period when the particle descends from

highest point to the position where its velocity vector makes an angle q/2 with horizontal, work done by the gravity force is

(A) mu2 tan2 q/2 (B) mu2 tan2 q

(C) mu2 cos2 q tan2q/2 (D) mu2 cos2 q/2 sin2q

2. A uniform chain of mass M and length L lies on a frictionless table with length l0 hanging over the edge. The chain beings to slide down. Then the speed with which the end slides away form the edge is given by

(A) v = (B) v =

(C) v = (D) v =

3. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a c is varying with time t as ac

= K2.r.t2, where k is a constant. The power delivered to the particle by the forces acting on it is(a) 2 mK2.r2.t (b) mK2.r2t (c) mK4.r2.t5/3 (d) zero

4. The relation between the displacement x and the time t for a body of mass 2 kg moving under the action of a force is given by x = ,

where x is in meters and t is in seconds. The work done by the body in the Ist 2 seconds is

(A) 1.6 J (B) 16 J

(C) 160 J (D) 1600 J

5. A block is attached to a horizontal spring of stiffness k. The other end of the spring is attached to a fixed wall. The entire system lie on a horizontal surface and the spring is in natural state. The natural length of the spring is l0. If the block is slowly lifted up

vertically to a height l0 from its initial position, which of the following is not correct?

(A) The work done by the gravity = mgl0

(B) The work done by the spring force = -

(C) The work done by the lifting force =

(D) The sum of works done by all the forces on the block is zero.

6. A bullet of mass 10 gm is fired from a rifle with a velocity of 800 m/s. After passing through a mud wall 180 cm thick, the velocity

drops to 100 m/s. The average resistance of the wall is

(A) 750 N (B) 1250 N (C) 1750 N (D) 2250 N

7. A body is gently dropped on a conveyor belt moving 3 m/s. If m = 0.5 how far will the body move relative to the belt before coming to rest? (g = 10m/s2)(a) 0.3 m (b) 0.6 m (c) 0.9 m (d) 0.8 m

8. A ball hits a horizontal surface with speed 10 m/s at an angle of incidence 30 o. If coefficient of restitution is 3

2 then distance between

the point of incidence and the point at which ball hits the plane second time is _____.

9. A man of mass m is standing on a plank mass M placed on smooth horizontal surface. If the man moves a distance x relative to the plank then distance moved by the centre of mass of the system is _________.

(A)

10. A block of mass M slides along the sides of a flat bottomed bowl. The side of the bowl are frictionless and the base has a coefficient of friction 0.2. If the block is released from the top of the side which is 1.5 m high, where will the block come to rest. Given, the length of the base PQ is 15 m(A) 1 m from P (B) mid point of flat part PQ(C) 2 m from P (D) at Q

11. A spring is compressed between two toy –carts of masses m1 and m2. When the toy –carts are released, the spring exerts on each toy-cart equal and opposite force for the same time t. If the coefficient of friction ‘m’ between the ground and the toy-carts are equal, then the displacements of the two toy-carts :

(A) (B)

(C) (D)

12. A force acting on the body is given by F = x2y + yx2 , where x and y are coordinates.

Then that force is(A) Conservative force (B) Non-Conservative force(C) Can’t say (D) none of these

13. A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to K

r2, where K is a constant. Then

KE of the particle will be

(a) K

r2(b) kr (c) 2k/r (d) k/2r

14. For a body of mass m moving on a straight line position is given as x = 4t2 + 3t + 5. Find the work done in 3 to 5 seconds.

(a) The change in the kinetic energy of a body must be equal to the sum of the works done by various forces acting on the body.

(b) The change in the total energy (kinetic + potential energy) is equal to the sum of works done by various forces acting on the

body.

(c) Potential energy is defined if and only if the force is such that the net work done on a body on a closed path is zero.

(d) If the force acting on a body is dependent on its velocity, then also it is possible to define its potential energy.

15. An engine pump is used to pump a liquid of density continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy imparted to the liquid is

(A) (B) (C) (D) Av

16. If momentum of a body is increased by 20 %, then kinetic energy increases by (A) 44 % (B) 55 % (C) 66 % (D) 77 5

17. A bullet is fired normally on a immovable wooden plank. It loses 25 % of its kinetic energy in penetrating a thickness x of the plank. What is the total thickness penetrated by the bullet ?(A) 2x (B) 4x (C) 6 x (D) 5x

18. A wind power generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy. For wind speed v, the electrical power output will be proportional to (A) v (B) v2 (C) v3 (D) v4

19. A ball is thrown up with a certain velocity at an angle q to the horizontal. The variation of its kinetic energy K.E. with respect to the horizontal displacement 'X' from the point of projection is best represented by :

(a)

(b)

(c)(d)

20. If a particle changes its position from (2m, 2m) to (4m, 4m) while the force N is acting on it, work done by the force

would be

(A) – 20J (B) 20J (C) 40J (D) 0J

21. Consider a body of mass (m) is moving on the frictionless surface as shown below. The velocity at bottom of surface i.e. at B is ________.

m

B

h

A

22. A particle moves under effect of a force F = cx from x = 0, to x = x1 . The work done on forces is

(a) Cx12 (b)

1

2 12Cx (c) Cx1

3 (d) zero

23. A body of mass 2.0 kg is at rest at height of 10 m above the ground. Calculate its P.E. and K.E. after it has fallen through half the height(a) 98 J, 98 J (b) 110 J, 120 J (c) 20 J, 40 J (d) 90 J, 30 J

24. The below given graph shows the force variation of spring force of a spring with stretching of spring. The change in potential energy is _______.

F(x) = Kx

x

25. If the force acting on a body is inversely proportional to its speed then K.E. of the body is (a) constant (b) directly proportional to time(c) inversely proportional to time (d) directly proportional to square of time

26. A cricket ball is hit at an angle q to the horizontal with a kinetic energy of k. The KE at highest point is (a) zero (b) Kcosq (c) Kcos2q (d) Ksec2q

27. The work done by external forces on a body equals the change in (a) KE only (b) PE only(c) Thermal energy only (d) Total energy

28. A position dependent force F = 7 - 2x + 3x2 N, acts on a small body of mass 2 kg and displaces it from x = 0 to x = 5m. The work done in Joules is (a) 35 (b) 40 (c) 135 (d) 270

29. If a light body A and a heavy body B have the same kinetic energy then ratio of the momentum of A to that of B (a) = 1 (b) > 1 (c) < 1 (d) can not be calculated

30. A ball of mass m is moving with speed u hits a wall of mass M (>> m) moving with speed v directly towards the ball. If impact is elastic then work done on the ball by the wall is ________.

31. The end of a pile of loose-link chain of mass per unit length f is being pulled horizontally along the surface by a constant force F. If the co-efficient of kinetic friction between the surface and the chain is m, then acceleration of the chain when length x is pulled will be _______.

x

32. A small ball of mass m is released from rest from height 2h to slide on smooth track which turns in a vertical of radius h. At the highest point speed of the ball will be _________. 2h

h

33. How much work is done in raising a stone of mass 5 Kg and relative density 3 lying at the bed of a lake through height of 3 metre? (Take g = 10 ms-2):(a) 25 J (b) 100 J (c) 75 J (d) None of the above

34. The equal retarding force is applied to stop a train. If the speed is doubled then the distance covered before being stopped will be (a) the same (b) doubled (c) half (d) four times

35. A ball is allowed to fall from a height of 10 m. If there is 40 % loss of energy due to impact, then after one impact the ball will go upto(a) 10 m (b) 8 m (c) 4 m (d) 6 m

36. Work done when a force F = ( + 2 + 3 ) N is acting on a particle to take it from the point = ( + + ) m and = ( +

2 )m is

(a) 3J (b) 1 J (c) Zero (d) 2 J

37. Two bodies of masses m1 and m2 have equal momentum. Their kinetic energy E1 and E2 are in the ratio

(a) m1 : m2 (b) m1 : m2 (c) m2 : m1 (d) :

38. The potential energy between two atoms in a molecule is given by U(x) = where a and b are positive constants and x is the

distance between the atoms. The atom is in stable equilibrium when

(A) x = (B) x =

(C) x = 0 (D)

39. One meter stick having mass 600 gm, is pivoted at one end. And is displaced through an angle of 60 , the increase in its potential energy is (g = 10 m/s2)(a) 1.5 J (b) 15 J (c) 150 J (d) 0.15 J

40. A block of mass M is lowered vertically by a cord through a distance d with constant acceleration g/4. The work done by cord on the block is

(a) (b) (c) mgd (d) none of these.

41. A light elastic cord of natural length OA is suspended from O. A load of mass 'm' is attached to A and released from the undeformed state of the cord. The mass oscillates vertically between A and B AB being equal to h. When the mass is at B, the potential energy stored in the cord is

( ) ( ) ( ) ( )a mgh b mgh

c mgh dmgh

22

2

42. When work is done ________ a ________ force on a body, the potential energy of the body by conservative decreases.

43. A solid sphere rolls down a parabolic path, whose vertical dimension y = kx2 and base of the parabola is at x = 0. During the fall, the sphere does not slip, but beyond the base the climb is frictionless. If the sphere falls a height h , the height above base that it would climb equals(a) h (b) (7/5)h (c) (5/7)h (d) none of these

44. The kinetic energy of a body moving with a speed of 10 m/s is 30 J. if its speed becomes 30 m/s its kinetic energy will be (a) 10 J (b) 90 J (c) 180 J (d) 270 J

45. When a body of mass M slides down an inclined plane of inclination q, through a distance s, the work done by surface is: (m is coefficient of friction)(A) m Mg cos q s (B) m Mg sin q s(C) Mg (m cos q- sin q)s (D) None of the above

46. If v, P and E denote the velocity, momentum and kinetic energy of the particle, then:(A) P = dE/dv (B) P = dE/dt(C) P = dv/dt (D) none of these

47. In the spring mass system shown in the figure, the spring is compressed by x0 = mg/3k from its natural length and the block is released from rest. The speed of the block , when it passes through the point P, is

(A) (B) g

(C) g (D) g

48. An object is acted upon by the forces N and N. If the displacement of the object is ( ) metre, the

kinetic energy of the object (A) remains constant (B) increases by 1 J(C) decreases by 1 J (D) decreases by 2J

49. When work done by force of gravity is negative, which of the following will definitely occur (A) Potential energy increases.(B) Kinetic energy decreases.(C) Gravitational Potential energy increases. (D) Gravitational Potential energy decreases.

50. A rod is allowed to fall down on the floor from vertical position. There is sufficient friction to prevent slipping at the end of the rod on the floor which of the following principle are applicable(A) conservation of energy (B) conservation of angular momentum(C) conservation of linear momentum (D) none of these

51. A point of application of a force F = is moved from to . The work done is

(a) –22 units (b) 22 units (c) 11 units (d) zero

52. A body of mass ‘m’ is connected to two springs of spring constants K 1 and K2 and is in equilibrium on a smooth horizontal surface as shown. If the body is displaced to the left by a small distance ‘x’ from the position shown, what is the velocity of the body as its passes this position again? (springs are massless)

(A) 0 (B)

(C) (K1 + K2)x (D) data insufficient

53. A lorry and a car moving with the same K.E. are brought to rest by the application of brakes which provide equal retarding force. Which of them will come to rest in a shorter distance (a) lorry will move shorter distance before coming to rest (b) car will move shorter distance before coming to rest (c) both will move same distance before coming to rest (d) can not be decided, since mass of the lorry or the car is not given.

54. Work done in time t on a body of mass m which is accelerated from rest to a speed v in time t 1 as a function of time t is given by

(a) 1

2 1

2mv

tt (b) m

v

tt

1

2

(c) 1

2 1

2

2mv

tt

(d)

1

2

2

12

2mv

tt

55. A block of mass m is released on the frictionless incline as shown from a height R. The incline turns in to a circle of radius R/2. The maximum height attained by the block is

(A) less than R/2 (B) greater than R/2(C) equal to R (D) less than R

56. A body of mass m is falling freely through a height h from the top of a tower. The velocity just before touching the ground is

. The work done by air drag is

(A) (B)

(C) Zero (D) None of the above

57. A block of mass 5 kg is allowed to slide on a frictionless wedge, free to move on a horizontal smooth surface. The increase in gravitational potential energy of block and wedge, when block reaches the bottom, is

(A) 500 J (B) 400 J(C) 300 J (D) none of the above

58. From a waterfall, is pouring down at the rate of 100kg per second on the blades of the turbine. If the height of the fall be 100m, the power delivered to the turbine is(A) 100KW (B) 10KW(C) 1 KW (D) 100W

59. A force where k is a positive constant acts on a particle moving in the x-y plane. Starting form the origin, the

particle is taken along positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the

force on the particle is

(A) -2ka2 (B) 2ka2 (C) –ka2 (D) ka2

60. A particle move in X- Y plane under the influence of a force such that its instantaneous momentum is

. What is the angle between the force and instantaneous momentum?

(A) 00C (B) 1800 (C) 900 (D) 450

61. A conservative force field is that field in which work done against _________ in transporting a test body along ________ equals ________.

62. A heavy particle is projected up from a point at angle with the horizontal. At any instant 't', if P = linear momentum, y = vertical displacement, x = horizontal displacement, then the kinetic energy of the particle plotted against these parameters can be

(a) (b)

(c)

(d)

63. The plot of velocity versus time is shown in the figure. A varying force acts on the body. The correct statement(s) among the following is (are)(A) in moving from A to B, work done on the body is negative.(B) in moving from B to C no work is done on the body.

(C) in moving from C to D, work done by the force on the body is positive.(D) in moving from D to E, work done by the force on body is positive.

1. C 2. 3. B 4. B

5. A 6 C 7. C 8.

9. 10. D 11. B 12.

13. ? 14.

15. A 16. A

17. B 18. B 19. 20. D

21. 22. B 23. A 24.

25. 26. C 27. D 28. C

29. B 30. 31. mmgh 32.

33. 34. D 35. D 36. B

37. C 38. D 39. A 40. D

41. A 42. 43. A 44. D

45. D 46. A 47. B 48. C

49. D 50. A 51. A 52. B

53. C 54. D 55. ? 56.

57. 58. 59. ? 60.

61. 62. 63.

Ot

K.E

O y

K.E

Ox

K.E

OP2

K.E