A solid cylinder and a disc of same radii are allowed to roll down a rough inclined plane from the top of a plane. The ratio of their times taken to reach the bottom of the inclined plane is

A mass $‘m’$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

If the density of material of a circular plate and a square plate as shown is same, the centre of mass of the composite 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 ........ $m/s$.

A spherical hollow is made in a lead sphere of radius $R$, such that its surface touches the outside surface of lead sphere and passes through the centre. What is the shift in the centre of mass of lead sphere due to the hollowing?

The angular momentum of a projectile projected at an angle $\theta $ with the horizontal with speed $u$ about the point of projection when it is at the highest point of its trajectory is