Work, Energy and Power

An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?

1. mv3
2. 12mv2
3. 12m2v2
4. 12mv3

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional forces are 10% of energy. How much power is generated by the turbine ? (g = 10 m/s2)

1. 12.3 kW
2. 7.0 kW
3. 8.1 kW
4. 10.2 kW

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