Work, Energy and Power

A vertical spring with force constant k is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d. The net work done in the process is

1. mg(h + d) - 12kd2
2. mg(h - d) - 12kd2
3. mg(h - d) + 12kd2
4. mg(h + d) + 12kd2

300 J of work is done in sliding a 2 kg block up an inclined plane of height 10 m. Work done against friction is (Take g = 10 m/s2)

1. 1000 J
2. 200 J
3. 100 J
4. zero

The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm the potential energy stored in it is

1. U/4
2. 4U
3. 8U
4. 16U

A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation s = 13t2, where t is in seconds. Work done by the force in 2 seconds is

1. 195 J
2. 519 J
3. 38 J
4. 83 J

A force F acting [figure] on an object varies with distance x as shown here. The force is in N and x in m. The work done by the force in moving the object from x = 0 to x = 6 m is

1. 18.0 J
2. 13.5 J
3. 9.0 J
4. 4.5 J

A particle of mass m1 is moving with a velocity v1 and another particle of mass m2 is moving with a velocity v2. Both of them have the same momentum but their different kinetic energies are E1 and E2 respectively. If m1 > m2 then :

1. E1 < E2
2. E1E2 = m1m2
3. E1 > E2
4. E1 = E2

A ball of mass 2 kg and another of mass 4 kg are dropped together from a 60 feet tall building. After a fall of 30 feet each towards earth, their respective kinetic energies will be in the ratio of

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

A mass of 0.5 kg moving with a speed of 1.5 m/s on horizontal smooth surface, collides with a nearly weightless spring of force constant k = 50 N/m. The maximum compression of the spring would be [figure]

1. 0.15 m
2. 0.12 m
3. 1.5 m
4. 0.5 m

When a long spring is stretched by 2 cm, its potential energy is U. If the spring is stretched by 10 cm, the potential energy stored in it will be

1. U/5
2. 5U
3. 10U
4. 25U

A stone is tied to a string of length l and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is

1. 2(u2 - gl)
2. u2 - gl
3. u - u2 - 2gl
4. 2gl