Work, Energy and Power · Question 27

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

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