One circular ring and one ciruclar disc, both are having the same mass and radius. the ratio of their moments of inertia about the axis passing through their centres and perpendicular to their planes, will be

A disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in figure. At any instant, for the lower most point of the disc -

Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant, then the speed of centre of mass of the system will be

In free space, a shell moving with velocity $60\,m/s$ along the positive $x$ -axis. When it  passes through origin, it explodes into two peices of mass ratio $1 : 2.$ After the  explosion, the velocity of the centre of mass is ........ $m/s$.

We have two spheres one of which is hollow and the other solid. They have identical masses and moment of inertia about their respectively diameters. The ratio of their radius is given by

In a gravity free space, a man of mass $M$ standing at a height $h$ above the floor, throws a ball of mass $m$ straight down with a speed $u$ . When the ball reaches the floor, the distance of the man above the floor will be