A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity $\omega$. A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of the system becomes triple. If $E$ be the initial Kinetic energy of the system, then final Kinetic energy will be $\frac{E}{x}$.The value of $x$ is $....$

A thin rod of length $L$ and mass $M$ is held vertically with one end on the floor and is allowed to fall. Find the velocity of the other end when it hits the floor, assuming that the end on the floor does not slip

A solid sphere is rolling down an inclined plane. Then the ratio of its translational kinetic energy to its rotational kinetic energy is

Two point masses of $0.3\ kg$ and $0.7\ kg$ are fixed at the ends of a rod of length $1.4\ m$  and of negligible mass. The rod is set rotating about an axis perpendicular  to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of  

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

An automobile engine develops $100\ kW$ when rotating at a speed of $1800\ rev/min$.  What torque does it deliver .......... $N-m$