A solid sphere rolls without slipping and presses a spring of spring constant $k$ as shown in figure. Then, the maximum compression in the spring will be
$v\sqrt {\frac{{2M}}{{3k}}} $
$v\sqrt {\frac{{2M}}{{5k}}} $
$v\sqrt {\frac{{5k}}{{7M}}} $
$v\sqrt {\frac{{7M}}{{5k}}} $
A rod of length $50\,cm$ is pivoted at one end. It is raised such that if makes an angle of $30^o$ fro the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in $rad\,s^{-1}$ ) will be $(g = 10\,ms^{-2})$
Moment of inertia of a body about a given axis is $1.5\, kg\, m^2$ Initially the body is at rest. In order to produce a rotational kinetic energy of $1200\, J$, the angular acceleration of $20\, rad/s^2$ must be applied about the axis of rotation for a duration of ......... $\sec$.
Write the formula of work done by torque in rotational rigid body about a the fixed axis.
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
A solid square plate is spun around different axes with the same angular speed. In which of the following choice of axis of rotation will the kinetic energy of the plate be the largest?