If $L, M$ and $P$ are the angular momentum, mass and linear momentum of a particle respectively which of the following represents the kinetic energy of the particle when the particle rotates in a circle of radius $R$
$\frac{{{L^2}}}{{2M}}$
$\frac{{{P^2}}}{{2MR}}$
$\frac{{{L^2}}}{{2M{R^2}}}$
$\frac{{MP}}{2}$
A solid cylinder $P$ rolls without slipping from rest down an inclined plane attaining a speed $v_p$ at the bottom. Another smooth solid cylinder $Q$ of same mass and dimensions slides without friction from rest down the inclined plane attaining a speed $v_q$ at the bottom. The ratio of the speeds $\frac{v_q}{v_p}$ is
A meter stick is held vertically with one end on the floor and is allowed to fall. The speed of the other end when it hits the floor assuming that the end at the floor does not slip is ......... $m / s$ $\left(g=9.8 \,m / s ^2\right)$
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
Consider two masses with $m_1 > m_2$ connected by a light inextensible string that passes over a pulley of radius $R$ and moment of inertia $I$ about its axis of rotation. The string does not slip on the pulley and the pulley turns without friction. The two masses are released from rest separated by a vertical distance $2 h$. When the two masses pass each other, the speed of the masses is proportional to