A bullet of mass $m$ moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a height $h$, the initial velocity of the bullet will be
$\sqrt {2gh} $
$\frac{{(M + m)}}{m}\sqrt {2gh} $
$\frac{m}{{(M + m)}}\sqrt {2gh} $
$\frac{{(M - m)}}{m}\sqrt {2gh} $
After on head on elastic collision between two balls of equal masses , one is observed to have a speed of $3\, m/s$ along positive $x$ -axis and the other has a speed of $2\, m/s$ along negative $x$ -axis. The original velocities of the balls are
A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $ac$ is varying with time t as $a_c = k^2rt^2$ where $k$ is a constant. The power delivered to the particle by the force acting on it
A neutron travelling with a velocity $v$ and $K.E.$ $E $ collides perfectly elastically head on with the nucleus of an atom of mass number $A$ at rest. The fraction of total energy retained by neutron is
A mass of $0.5\, kg$ moving with a speed of $1.5\, m/s$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k=50\,N/m$. The maximum compression of the spring would be ................. $\mathrm{m}$