A disc of mass $M$ and radius $R$ rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is $v$, the height to which the disc will rise will be
$\frac {3v^2}{2g}$
$\frac {3v^2}{4g}$
$\frac {v^2}{4g}$
$\frac {v^2}{2g}$
A body of mass $m= 10^{-2} \;kg$ is moving in a medium and experiences a frictional force $F= -kv^2$ Its intial speed is $v_0= 10$ $ms^{-1}$ If, after $10\ s$, its energy is $\frac{1}{8}$ $mv_0^2$ the value of $k$ will be
The bob of a pendulum of length $l$ is pulled aside from its equilibrium position through an angle $\theta $ and then released. The bob will then pass through its equilibrium position with speed $v$ , where $v$ equals
A ball of mass $M$ falls from a height $h$ on a floor which the coefficient of restitution is $e$. The height attained by the ball after two rebounds is
A ball moving with velocity $2\, m/s$ collides head on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in $m/s$) after collision will be
When a constant force is applied to a body moving with constant acceleration, power does not remain constant. For power to be constant, the force has to vary with speed as follows