$A$ constant power is supplied to a rotating disc. The angular velocity $(\omega)$ of the disc varies with the number of rotations $(n)$ made by the disc as:

$A$ thin rod of mass $m$ and length $l$ is oscillating about a horizontal axis through its one end. Its maximum angular speed is $\omega$. Its centre of mass will rise up to a maximum height of:

$A$ thin uniform rod $AB$ of mass $m$ and length $l$ is hinged at one end $A$ to the ground level. Initially,the rod stands vertically and is allowed to fall freely to the ground in the vertical plane. The angular velocity of the rod when its end $B$ strikes the ground is ($g$ = acceleration due to gravity).

$A$ uniform rod of length $L$ is free to rotate in a vertical plane about a fixed horizontal axis through $B$. The rod begins rotating from rest from its unstable equilibrium position. When it has turned through an angle $\theta$,its angular velocity $\omega$ is given as

The $M.I.$ of a body about a given axis is $1.2 \ kg \cdot m^2$ and initially the body is at rest. In order to produce a rotational kinetic energy of $1500 \ J$,an angular acceleration of $25 \ rad/s^2$ must be applied about that axis for a time duration of $....... \ s$.

$A$ thin uniform metal rod of mass $M$ and length $L$ is swinging about a horizontal axis passing through its end. Its maximum angular velocity is $\omega$. Its centre of mass rises to a maximum height of (where $g$ is the acceleration due to gravity):