A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{sph}$ and $h_{cyl}$ on the incline. The radio $\frac{{{h_{sph}}}}{{{h_{cyl}}}}$ is given by

To maintain a rotor at a uniform angular speed of $100\, rad\, s^{-1}$, an engine needs to transmit torque of $100\, Nm$. The power of the engine is

Two bodies have their moments of inertia $I$ and $2 I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momentum will be in the ratio

If the rotational kinetic energy of a body is increased by $300\ \%$ then the percentage increase in its angular momentum will be .......... $\%$

$A$ sphere of mass $M$ and radius $R$ is attached by a light rod of length $l$ to $a$ point $P$. The sphere rolls without slipping on a circular track as shown. It is released from the horizontal position. the angular momentum of the system about $P$ when the rod becomes vertical 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