Work, Energy and Power · Question 42

An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 m/s. The mass per unit length of water in the pipe is 100 kg/m. What is the power of the engine?

1. 400 W
2. 200 W
3. 100 W
4. 800 W

A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be

1. 2Mg/k
2. 4Mg/k
3. Mg/2k
4. Mg/k

A body of mass 1 kg is thrown upwards with a velocity 20 m s-1. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction? ( g = 10 m s-2)

1. 30 J
2. 40 J
3. 10 J
4. 20 J

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