Work, Energy and Power

A particle moves from a point (-2 i+5 j ) to (4 j+3 k ) when a force of (4 i+3 j ) N is applied. How much work has been done by the force ?

1. 8 J
2. 11 J
3. 5 J
4. 2 J

A ball is thrown vertically downwards from a height of 20 m with an initial velocity v0. It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v0 is (Take g = 10 m s-2)

1. 28 m s-1
2. 10 m s-1
3. 14 m s-1
4. 20 m s-1

On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle to its initial direction and has a speed v3. The second block's speed after the collision is

1. 3 2v
2. 32v
3. 2 23v
4. 34v

A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is

1. 2mk t-1/2
2. 12 mk t-1/2
3. mk2 t-1/2
4. mk t-1/2

A block of mass 10 kg, moving in x direction with a constant speed of 10 m s-1, is subjected to a retarding force F = 0.1x J/m during its travel from x = 20 m to 30 m. Its final KE will be

1. 275 J
2. 250 J
3. 475 J
4. 450 J

Two particles of masses m1, m2 move with initial velocities u1 and u2. On collision, one of the particles gets excited to higher level, after absorbing energy . If final velocities of particles be v1 and v2 then we must have :

1. 12m1u12 + 12m2u22 - = 12m1v12 + 12m2v22
2. 12m12u12 + 12m22u22 + = 12m12v12 + 12m22v22
3. m12u1 + m22u2 - = m12v1 + m22v2
4. 12m1u12 + 12m2u22 = 12m1v12 + 12m2v22 -

Two similar springs P and Q have spring constants KP and KQ, such that KP > KQ. They are stretched first by the same amount (case a), then by the same force (case b). The work done by the springs WP and WQ are related as, in case (a) and case (b) respectively

1. WP > WQ; WQ > WP
2. WP < WQ; WQ < WP
3. WP = WQ; WP > WQ
4. WP = WQ; WP = WQ

The upper half of an inclined plane of inclination is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by

1. = 2
2. =
3. = 1
4. = 2

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