Work, Energy and Power

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