$A$ block of mass $m$ is moving with a velocity $u$ on a smooth horizontal surface towards a wedge of same mass $m$ initially kept at rest. The wedge is free to move in any direction. Initially, the block moves up the smooth inclined plane of the wedge to a height $h$ and then moves down back to the horizontal plane. In this process, the wedge gains a velocity equal to:

Under the influence of mutual internal forces,which of the following is true for a system?

$A$ jet engine works on the principle of

$A$ cannon shell fired breaks into two equal parts at its highest point. One part retraces the path to the cannon with kinetic energy $E_1$ and the kinetic energy of the second part is $E_2$. The relation between $E_1$ and $E_2$ is:

$A$ ball of mass $200\,g$ rests on a vertical post of height $20\,m$. $A$ bullet of mass $10\,g$,travelling in a horizontal direction,hits the centre of the ball. After the collision,both travel independently. The ball hits the ground at a distance of $30\,m$ and the bullet at a distance of $120\,m$ from the foot of the post. The value of the initial velocity of the bullet will be $............m/s$ (if $g = 10\,m/s^2$).

$A$ bomb of mass $3m \text{ kg}$ explodes into two pieces of mass $m \text{ kg}$ and $2m \text{ kg}$. If the velocity of the $m \text{ kg}$ mass is $16 \text{ m/s}$,the total kinetic energy released in the explosion is ................. $m \text{ J}$.