$A$ bullet is fired from a rifle. If the rifle recoils freely,then the kinetic energy of the rifle is

$A$ body of mass $14 \ kg$ initially at rest explodes and breaks into three fragments of masses in the ratio $2:2:3$. The two pieces of equal masses fly off perpendicular to each other with a speed of $18 \ m/s$ each. The velocity of the heavier fragment is . . . . . . $m/s$.

$A$ vessel at rest explodes into three pieces. Two pieces having equal masses $m$ fly off perpendicular to one another with the same velocity $30 \, m/s$. The third piece has three times the mass of each of the other pieces. The magnitude and direction of the velocity of the third piece will be:

$A$ shell initially at rest explodes into two pieces of equal mass. Then the two pieces will:

The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. The velocity of the man with respect to ground $v_1$ will be

$A$ man of mass $m$ is standing on a cart of mass $2m$. Initially, the cart is at rest. The man jumps horizontally with a relative velocity $u$ with respect to the cart. The work done by the internal forces of the man during the process of jumping will be: