The grinding stone of a flour mill is rotating at $600\, rad/sec$. for this power of  $1.2\, k\, watt$ is used. the effective torque on stone in $N-m$ will be

Two discs of moments of inertia $I_1$ and $I_2$ about their respective axes (normal to  the disc and passing through the centre), and rotating with angular speed $\omega _1$ and $\omega _2$ are  brought into contact face to face with their axes of rotation coincident. What is the  loss in kinetic energy of the system in the process ?

A metal sphere of radius $r$ and specific heat $S$ is rotated about an axis passing through its centre at a speed of $f$ rotations per second. It is suddenly stopped at $50\%$ of its energy is used in increasing its temperature. Then the rise in temperature of the sphere is

A small object of uniform density rolls up a curved surface with an initial velocity $v$. It reaches up to a maximum height of $\frac{3 \mathrm{v}^2}{4 \mathrm{~g}}$ with respect to the initial position. The object is

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $3\, m / s$ (as shown in figure). Maximum height with respect to the initial position covered by it will be $...........cm$.

A disc and a ring of same mass are rolling and if their kinetic energies are equal, then the ratio of their velocities will be