A solid sphere of mass $2\,kg$ is making pure rolling on a horizontal surface with kinetic energy $2240\,J$. The velocity of centre of mass of the sphere will be $..........ms ^{-1}$.

A solid sphere rolls without slipping and presses a spring of spring constant $k$ as shown in figure. Then, the maximum compression in the spring will be

A solid sphere rolls without slipping, first horizontally and then up to a point $X$ at height $h$ on an inclined plane before rolling down, as shown in the figure below. The initial horizontal speed of the sphere is

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is $50 \,\%$ of its translational kinetic energy. The body is :

A ring, a solid sphere and a thin disc of different masses rotate with the same kinetic energy. Equal torques are applied to stop them. Which will make the least number of rotations before coming to rest

A cord is wound round the circumference of wheel of radius $r$. The axis of the wheel is horizontal and the moment of inertia about it is $I. \,A$ weight $mg$ is attached to the cord at the end. The weight falls from rest. After falling through a distance $ 'h '$, the square of angular velocity of wheel will be ..... .