Work, Energy and Power

A uniform force of (3 i + j) newton acts on a particle of mass 2 kg. Hence the particle is displaced from position (2 i + k) metre to position (4 i + 3 j - k) metre. The work done by the force on the particle is

1. 13 J
2. 15 J
3. 9 J
4. 6 J

A particle with total energy E is moving in a potential energy region U(x). Motion of the particle is restricted to the region when

1. U(x) < E
2. U(x) = 0
3. U(x) E
4. U(x) > E

One coolie takes 1 minute to raise a suitcase through a height of 2 m but the second coolie takes 30 s to raise the same suitcase to the same height. The powers of two coolies are in the ratio

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

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P0. The instantaneous velocity of this car is proportional to

1. t2P0
2. t1/2
3. t-1/2
4. t m

The potential energy of a particle in a force field is U = Ar2 - Br where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is

1. B2A
2. 2AB
3. AB
4. BA

Two spheres A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction:

1. same as that of B
2. opposite to that of B
3. = -1 ( 12 ) to the x-axis
4. = -1 (- 12 ) to the x-axis

A mass m moving horizontally (along the x-axis) with velocity v collides and sticks to a mass of 3m moving vertically upwards (along the y-axis) with velocity 2v. The final velocity of the combination is

1. 32v i + 14v j
2. 14v i + 32v j
3. 13v i + 23v j
4. 23v i + 13v j

The potential energy of a system increases if work is done

1. upon the system by a nonconservative force
2. by the system against a conservative force.
3. by the system against a nonconservative force.
4. upon the system by a conservative force.

A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest

1. at the highest position of the body
2. at the instant just before the body hits the earth.
3. it remains constant all through.
4. at the instant just after the body is projected.

Force F on a particle moving in a straight line varies with distance d as shown in figure. [figure] The work done on the particle during its displacement of 12 m is

1. 18 J
2. 21 J
3. 26 J
4. 13 J

A particle of mass M, starting from rest, undergoes uniform acceleration. If the speed acquired in time T is V, the power delivered to the particle is

1. MV2T
2. 12 MV2T2
3. MV2T2
4. 12 MV2T

A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be

1. 0, 1
2. 1, 1
3. 1, 0.5
4. 0, 2

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

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

If kinetic energy of a body is increased by 300% then percentage change in momentum will be :

1. 100%
2. 150%
3. 265%
4. 73.2%

250 N force is required to raise 75 kg mass from a pulley. If the rope is pulled 12 m, then the load is lifted 3 m. The efficiency of the pulley system will be

1. 25%
2. 33.3%
3. 75%
4. 90%

A child is sitting on a swing. Its minimum and maximum heights from the ground are 0.75 m and 2 m respectively, its maximum speed will be

1. 10 m/s
2. 5 m/s
3. 8 m/s
4. 15 m/s