A thin rod of mass $m$ and length $l$ is oscillating about horizontal axis through its one end. Its maximum angular speed is $\omega$. Its centre of mass will rise upto maximum height :-
$\frac{1}{6} \frac{l \omega}{g}$
$\frac{1}{2} \frac{l^2 \omega^2}{g}$
$\frac{1}{6} \frac{l^2 \omega^2}{g}$
$\frac{1}{3} \frac{l^2 \omega^2}{g}$
A ring of mass $m$ and radius $r$ rotates about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$. Its kinetic energy is
A uniform cylinder of radius $R$ is spinned with angular velocity $\omega$ about its axis and then placed into a corner. The coefficient of friction between the cylinder and planes is $μ$. The number of turns taken by the cylinder before stopping is given by
A circular disc of moment of inertia $I_t$, is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\omega_i$ . Another disc of moment of inertia $l_b$ is dropped coaxially onto the rotating disc. Initially the second disc has zero angular speed. Eventually both the discs rotate with a constant angular speed $\omega_f$. The energy lost by the initially rotating disc to friction is
A solid sphere is rolling down an inclined plane. Then the ratio of its translational kinetic energy to its rotational kinetic energy 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