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 :-

- A
$\frac{1}{6} \frac{l \omega}{g}$

- B
$\frac{1}{2} \frac{l^2 \omega^2}{g}$

- C
$\frac{1}{6} \frac{l^2 \omega^2}{g}$

- D
$\frac{1}{3} \frac{l^2 \omega^2}{g}$

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

- [AIPMT 2013]

A particle performs uniform circular motion with an angular momentum $L.$ If the angular frequency of the particle is doubled and kinetic energy is halved, its angular momentum becomes

- [AIEEE 2003]

Starting from the rest, at the same time, a ring, a coin and a solid ball of same mass roll down an incline without slipping .The ratio of their translational kinetic energies at the bottom will be

Two uniform similar discs roll down two inclined planes of length $S$ and $2S$ respectively as shown is the fig. The velocities of two discs at the points $A$ and $B$ of the inclined planes are related as

Two rotating bodies $A$ and $B$ of masses $m$ and $2\,m$ with moments of inertia $I_A$ and $I_B (I_B> I_A)$ have equal kinetic energy of rotation. If $L_A$ and $L_B$ be their angular momenta respectively, then

- [NEET 2016]