Two bodies with masses $M_1$ and $M_2$ have equal kinetic energies. If $p_1$ and $p_2$ are their respective momenta, then $p_1/p_2$ is equal to

A bag of sand of mass $M$ is suspended by a string. A bullet of mass $m$ is fired at it with velocity $v$ and gets embedded into it. The loss of kinetic energy in this process is

A body of mass $m$ is projected from ground with speed $u$ at an angle $\theta$ with horizontal. The power delivered by gravity to it at half of maximum height from ground is

$A$ ball is dropped from $a$ height $h$. As it bounces off the floor, its speed is $80$ percent of what it was just before it hit the floor. The ball will then rise to $a$ height of most nearly .............. $\mathrm{h}$

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

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