Two blocks $A$  and  $B$  of masses  $1\,\,kg$  and  $2\,\,kg$  are connected together by a spring and are resting on a horizontal surface. The blocks are pulled apart so as to stretch the spring and then released. The ratio of  $K.E.s$  of both the blocks is

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

The work done by a force $\vec F = \left( { - 6{x^3}\hat i} \right)\,N$ in displacing a particle from $x = 4\,m$ to $x = -2\,m$ is ............... $\mathrm{J}$

Curve between net forcevs time is shown Initially particle is at rest .. Which of the following best represents the resulting velocity-time graph of the particle ?

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

$A$ particle of mass $m$ is released from $a$ height $H$ on $a$ smooth curved surface which ends into a vertical loop of radius $R$, as shown The minimum value of $H$ required so that the particle makes a complete vertical circle is given by