A sphere of mass m moving with constant velocity hits another sphere of the same mass at rest. If e is the coefficient of restitution. The ratio of their velocities after the collision is
1. 1 + e
2.
3.
4.
A particle is moving in a vertical circle. The tension in the string when passing through two positions at angle of 30 and 60 from vertical (the lowest position) are respectively, then:
1.
2.
3.
4. Tension in the string always remains the same.
A body is thrown vertically up with a certain initial velocity. The potential and the kinetic energy of the body are equal at a point P in its path. If the same body is thrown with double the velocity upwards, the ratio of the potential and the kinetic energies of the body when it crosses at the same point will be:
1. 1:1
2. 1:4
3. 1:7
4. 1:8
A body is displaced from (0,0) to (1m,1m) along the path x=y by a force . The work done by this force will be :
1.
2.
3.
4.
A stone is projected from a horizontal plane. It attains maximum height, 'H', and strikes a stationary smooth wall & falls on the ground vertically below the maximum height. Assuming the collision to be elastic, the height of the point on the wall where the ball will strike will be:
1. | \(\frac{H}{2} \) | 2. | \(\frac{H}{4} \) |
3. | \(\frac{3 H}{4} \) | 4. | None of these |
A weightless rod of length 2l carries two equal mass 'm', one tied at lower end A and the other at the middle of the rod at B. The rod can rotate in a vertical plane about a fixed horizontal axis passing through C. The rod is released from rest in the horizontal position. The speed of the mass B at the instant rod becomes vertical is:
(1)
(2)
(3)
(4)
A body of mass (m) elastically collides with another stationary body of mass 3m. The fractional loss of K.E. of the body is:
1.
2.
3.
4.
A force F is applied on a body which moves with a velocity v in the direction of the force, then the power will be
1.
2. Fv
3.
4. F/v
Potential energy (U) related to coordinates is given by U = 3(x + y). Work done by the conservative force when the particle is going from (0, 0), (2, 3) is:
1. 15 J
2. -15 J
3. 12 J
4. 10 J
A mass of 0.5kg moving with a speed of 1.5 m/s on a horizontal smooth surface collides with a nearly weightless spring of force constant k = 50 N/m. The maximum compression of the spring would be
1. 0.5 m
2. 0.15 m
3. 0.12 m
4. 1.5 m