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 student of mass $M$ is $1.5 \,m$ tall and has her centre of mass $1 \,m$ above ground when standing straight. She wants to jump up vertically. To do so. she bends her knees so that her centre of mass is lowered by $0.2 \,m$ and then pushes the ground by a constant force F. As a result, she jumps up such that the maximum height of her feet is $0.3 \,m$ above ground. The ratio $F / Mg$ 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
The speed of a homogeneous solid sphere after rolling down an inclined plane of vertical height $h$, from rest without sliding, 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 $...........cm$.
Write the formula for power and angular momentum in rotational motion.