Work, Energy and Power · Question 11

A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively -

1. S4, 3gS2
2. S4, 3gS2
3. S4, 3gS2
4. S2, 3gS2

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

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

A force F = 20 + 10y acts on a particle in y-direction where F is in newton and y in meter. Work done by this force to move the particle from y = 0 to y = 1 m is :

1. 5 J
2. 25 J
3. 20 J
4. 30 J

A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when :

1. the wire is horizontal
2. inclined at an angle of 60 from vertical
3. the mass is at the lowest point
4. the mass is at the highest point

Body A of mass 4m moving with speed u collides with another body B of mass 2 m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is :

1. 59
2. 49
3. 89
4. 19

A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be

1. 0.5
2. 0.25
3. 0.8
4. 0.4

A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB = D. The height h is equal to [figure]

1. D
2. 32D
3. 75D
4. 54D

Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m s-1. Take 'g' constant with a value 10 m s-2. The work done by the (i) gravitational force and the (ii) resistive force of air is

1. (i) 1.25 J (ii) -8.25 J
2. (i) 100 J (ii) 8.75 J
3. (i) 10 J (ii) -8.75 J
4. (i) -10 J (ii) -8.25 J

A body of mass 1 kg begins to move under the action of a time dependent force F = (2t i + 3t2 j) N, where i and j are unit vectors along x and y axis. What power will be developed by the force at the time t?

1. (2t3 + 3t4) W
2. (2t3 + 3t5) W
3. (2t2 + 3t3) W
4. (2t2 + 4t4) W

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

1. 3gR
2. 5gR
3. gR
4. 2gR