If the angular momentum of a body is increased by $200\,\%$ then increase in its rotational kinetic energy will be ....... $\%$.

The plank in the figure moves a distance $100\,mm$ to the right while the centre of mass of the sphere of radius $150\, mm$ moves a distance $75\,mm$ to the left. The angular displacement of the sphere (in radian) is  (there is no slipping anywhere) :-

Three bodies , a ring, a solid cylinder and a solid sphere roll down the same inclined  plane without slipping. They start from rest. The radii of the bodies are identical. Which  of the bodies reaches the ground with maximum velocity?

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 ........ $m.$

Two particles $A$ and $B$ initially at rest move towards each other under a mutual force of attraction. At the instant when the speed of $A$ is $v$ and the speed of $B$ is $2v$, the speed of centre of mass of the system is

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