Work, Energy and Power

A force f=x2y i+y2 j acts on a particle in a plane x+y=10. The work done by this force during a displacement from (0,0) to (4 m,2 m) is Joule (round off to the nearest integer)

A bob of mass m is suspended at a point O by a light string of length l and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity v0 at the point ' A ', the string becomes slack when the bob reaches at the point ' D '. The ratio of the kinetic energy of the bob at the points B and C is . [figure]

1. 4
2. 1
3. 2
4. 3

A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is 10 m/s. The ratio of its kinetic energies at point B and C is : [figure] (Take acceleration due to gravity as 10 m/s2)

1. 3- 22
2. 2+ 33
3. 2+ 23
4. 3+ 32

A ball of mass 100 g is projected with velocity 20 m/s at 60 with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is

1. 20 J
2. 5 J
3. 15 J
4. zero

A force F=2 i+b j+ k is applied on a particle and it undergoes a displacement i-2 j- k. What will be the value of b, if work done on the particle is zero.

1. 13
2. 12
3. 0
4. 2

A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation v = x, where is a constant. The total work done by all the forces applied on the particle during its displacement from x = 0 to x = d, will be :

1. m2 2 d
2. md2 2
3. m 2 d2
4. 2m 2 d

A force (3x2 + 2x - 5) N displaces a body from x = 2 m to x = 4 m. Work done by this force is J.

Three bodies A, B and C have equal kinetic energies and their masses are 400 g, 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is :

1. 1 : 3 : 2
2. 3 : 2 : 1
3. 1 : 3 : 2
4. 2 : 3 : 1

[figure] A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :

1. 6 m
2. 5 m
3. 1 m
4. 2 m

A bullet of mass 50 g is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is :

1. 44\%
2. 16\%
3. 84\%
4. 32\%

Four particles A, B, C, D of mass m2, m, 2m, 4m, have same momentum, respectively. The particle with maximum kinetic energy is :

1. B
2. C
3. D
4. A

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be :

1. 60%
2. 500%
3. 6%
4. 600%

A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be : [figure]

1. 2 : 1
2. 3 : 2
3. 1 : 1
4. 1 : 2

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :

1. t2/3
2. t3/2
3. t
4. t2

If a rubber ball falls from a height h and rebounds upto the height of h/2. The percentage loss of total energy of the initial system as well as velocity of ball before it strikes the ground, respectively, are :

1. 50\%, 2gh
2. 50\%, gh
3. 50\%, gh2
4. 40\%, 2gh

A body of m kg slides from rest along the curve of vertical circle from point A to B in frictionless path. The velocity of the body at B is: [figure] (given, R = 14 m, g = 10 m/s2 and 2 = 1.4)

1. 10.6 m/s
2. 19.8 m/s
3. 16.7 m/s
4. 21.9 m/s

A simple pendulum of length 1 m has a wooden bob of mass 1 kg. It is struck by a bullet of mass 10-2 kg moving with a speed of 2 102 ms-1. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is : (use g=10 m/s2)

1. 0.20 m
2. 0.40 m
3. 0.30 m
4. 0.35 m

A body of mass 2 kg begins to move under the action of a time dependent force given by F= (6t i+6t2 j ) N. The power developed by the force at the time t is given by:

1. (3t3+6t5 ) W
2. (9t5+6t3 ) W
3. (6t4+9t5 ) W
4. (9t3+6t5 ) W

A particle is placed at the point A of a frictionless track ABC as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point B is : (Take g=10 m/s2). [figure]

1. 2 10 m/s
2. 10 m/s
3. 10 m/s
4. 20 m/s

A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of 60 by a force of 10 N parallel to the inclined surface as shown in figure. When the block is pushed up by 10 m along inclined surface, the work done against frictional force is : [g=10 m/s2] [figure]

1. 5 3 J
2. 5 J
3. 5 103 J
4. 10 J

A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction (in J) is :

1. 3900
2. 4500
3. 4200
4. 4000

The potential energy function (in J) of a particle in a region of space is given as U= (2x2+3y3+2z ). Here x, y and z are in meter. The magnitude of x-component of force (in N) acting on the particle at point P(1,2,3) m is :

1. 4
2. 2
3. 8
4. 6

A bob of mass 'm' is suspended by a light string of length 'L'. It is imparted a minimum horizontal velocity at the lowest point A such that it just completes half circle reaching the top most position B. The ratio of kinetic energies (K.E)A(K.E)B is : [figure]

1. 5 : 1
2. 3 : 2
3. 1 : 5
4. 2 : 5

The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m. If it dissipates 10\% of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use, g=10 m s-2]

1. 5 6 m s-1
2. 5 5 m s-1
3. 2 5 m s-1
4. 6 5 m s-1

Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

1. 3:5
2. 5:4
3. 2:5
4. 4:5

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle ( ) of thread deflection in the extreme position will be :

1. -1 ( 12 )
2. 2 -1 ( 12 )
3. 2 -1 ( 1 5 )
4. -1 ( 2 )