1. A piece of wire is bent in the shape of a parabola y = kx^2 (y–axis vertical) with a bead of mass m on it. The
bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at
rest. The wire is now accelerated parallel to the x–axis with constant acceleration a. The distance of the
new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, form the y–
axis is
2.A uniform rod of length L and mass M is pivoted at the centre. Its two ends are attached to two springs of equal spring constants k. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle θ in one direction and released. The frequency of oscillation is
3.Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are v and 2v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A,
these two particles will again reach the point A ?
4.The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is
5.A rod of mass m and length
is hinged to its one end and held vertical. A point mass m is attached to the other end, is allowed to rotate about the hinge. The velocity of the particle when rod becomes horizontal is:6. A uniform rod A B of length L is hinged at one end A. The rod is kept in the horizontal position by a mass less string tied to point B as shown in figure. If the string is cut, the initial angular acceleration of the rod will be:
7.A straight bar, of mass 15 kg and length 2 m, at rest on a frictionless horizontal surface, receives an instantaneous impulse of 7.5 Ns perpendicular to the bar. If the impulse is applied at the centre of mass of the bar, the energy transferred is:
8. A satellite of mass m is orbiting the earth in a circular path of radius r with velocity v. How much energy is required to take the satellite from an orbit of radius r to one of radius 3 r :
9. In figure, a block slides down a frictionless inclined plane and a sphere rolls without sliding down a ramp of the same angle 
. The block and sphere have the same mass, start from rest at point A, and descend to point B
. The block and sphere have the same mass, start from rest at point A, and descend to point B
If work done by gravitational force on the block is W1 and that on sphere is W2, then:
10. In figure, a block slides down a friction less inclined plane and a sphere rolls without sliding down a ramp of the same angle . The block and sphere have the same mass, start from rest at point A, and descend to point B
. The block and sphere have the same mass, start from rest at point A, and descend to point BIn the previous problem, if v1 is the speed of block at B and v2 is the speed of sphere at the same position, then:
11. A block of mass of 1 kg slides down a curved track that is one quadrant of a circle of radius 1 m. Its speed at the bottom is 2 m/s. The work done by the frictional force is:
12.An object is attached to a vertical spring and slowly lowered to its equilibrium position. This stretches the spring by x. If the same object is attached to the same vertical spring but permitted to fall suddenly, the spring stretches by:
13.A body of mass m accelerates uniformly from rest to velocity v1 in time t1. The instantaneous power delivered to the body is:
14.A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of 
with the initial vertical direction is:
with the initial vertical direction is:15.The potential energy of 1 kg particle free to move along the x-axis is given by 
J. The total mechanical energy of the particle is 2 J then, the maximum speed in (m/s) is:
J. The total mechanical energy of the particle is 2 J then, the maximum speed in (m/s) is:16.Two springs A and B are identical except that A is stiffer than B, i.e., KA > KB.
The springs are stretched by equal amount of force. If WA and WB are the work done on them respectively then:
17.A particle of mass 4m which is at rest explodes into three fragments. Two of fragments, each of mass m are found to move with a speed v each in mutually perpendicular directions. The total energy released in the process is:
18.A ball 
of mass 1 kg, moving with speed of 12 m/s, collides obliquely and elastically with another ball B which was initially at rest. Ball A then moves off at right angles to its direction with a speed of 5m/s. The momentum of ball B after collision is:
of mass 1 kg, moving with speed of 12 m/s, collides obliquely and elastically with another ball B which was initially at rest. Ball A then moves off at right angles to its direction with a speed of 5m/s. The momentum of ball B after collision is:19. The rear block moves with a speed of 2 m/s towards the front block kept at rest on smooth surface. The spring is massless and having force constant 50 N/m. The maximum compression of the spring if each block is of 1 kg mass:
20. A ball is dropped on smooth inclined plane and is observed to move horizontally after the impact. The coefficient of restitution between plane and ball is e.
The inclination 
is:
is:21. A ball is dropped on smooth inclined plane and is observed to move horizontally after the impact. The coefficient of restitution between plane and ball is e.
