Four particles of masses $m_1 = 2m, m_2 = 4m, m_3 = m$ and $m_4$ are placed at four corners of a square. What should be the value of $m_4$ so that the centres of mass of all the four particles are exactly at the centre of the square ?

A rigid body is rotating with variable angular velocity $(a -bt)$  at any instant of time $t.$  The total angle subtended by it before coming to rest will be ( $a$  and $b$  are constants)

A disc initially at rest, is rotated about its axis with a uniform angular acceleration. In the first $2$ $s$ , it rotates an angle $\theta$. In the next $2\, s$, the disc will rotate through an angle

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 man of $50\, kg$ mass is standing in a gravity free space at a heigth of $10\,m$ above the floor. He throws a stone of $0.5\, kg$ mass downwards with a speed of $2\,m/s$. When the stone reaches the floor, the distance of the man above the floor will be ........ $m.$

Radius of gyration of a body depends on