A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After collision their final velocities are V and v respectively. The value of v is

The time constant of charging of the circuit shown in figure is

A rod AB of length 2 m and mass 2 kg is lying on a smooth horizontal x-y plane with its centre at origin O as shown in figure. An impulse J of magnitude 10 N-s is applied perpendicular to AB at A.

The distance of point P from centre of the rod which is at rest just after impact is

For two samples of ideal gases A and B curves are plotted n vs V (volume of container ) at 16.42 atm pressure. Then temperature of A and B respectively are:

A ballet dancer is rotating at angular velocity $\omega$ on smooth horizontal floor. The ballet dancer folds his body close to his axis of rotation by which his radius of gyration decreases by $1/4^{th}$ of his initial radius of gyration, his final angular velocity is

A uniform rod of length $L$ lies on a smooth horizontal table. The rod has a mass $M.$ A particle of mass $m$ moving with speed $v$ strikes the rod perpendicularly at one of the ends of the rod sticks to it after collision.
Find the velocity of the centre of mass $C$ and the angular, velocity of the system about the centre of mass after the collision.

From a circular disc of radius R and mass 9 M , a small disc of radius R/3 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is

A cubical block of side a is moving with velocity V on a horizontal smooth plane as shown in Figure. It hits a ridge at point O. The angular speed of the block after it hits O is

A slender uniform rod of mass $M$ and length $l$ is pivoted at one ens so that it can rotate in a vertical plane, Fig. There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $\theta$ with the vertical is

A balloons of mass M is descending at a constant acceleration $\alpha .$ When a mass m is released from the balloon, it starts rising. With the same acceleration $\alpha .$ Assuming that its volumes does not change, what is the valule of m?