$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be

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 time taken by the man to reach the other end is

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

State the law of conservation of total linear momentum for a system of particles.

$A$ bullet of mass $m$ is fired from a rifle of mass $M$. If $v$ is the velocity of the bullet,the velocity acquired by the rifle is:

$A$ bomb at rest in the air explodes into two fragments. If one fragment moves vertically upwards with a velocity $v_0$,in which direction will the other fragment move?