A disc of mass $1\,kg$ and radius $R$ is free of rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, its angular speed will be $4 \sqrt{\frac{x}{3 R}}$ rad s$^{-1}$ where $x=$
$\left( g =10\,ms ^{-2}\right)$
$50$
$8$
$5$
$88$
The ratio of rotational and translatory kinetic energies of a sphere is
To maintain a rotor at a uniform angular speed of $200 \;rad s^{-1}$, an engine needs to transmit a torque of $180 \;N m .$ What is the power required by the engine?
(Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is $100 \%$ efficient.
A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy $(K_t)$ as well as rotational kinetic energy $(K_r)$ simultaneously. The ratio $K_t : (K_t + K_r)$ for the sphere is
A tangential force $F$ is applied on a disc of radius $R$, due to which it deflects through an angle $\theta $ from its initial position. The work done by this force would be
Write the formula for rotational kinetic energy.