$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into two pieces. If one of those parts having mass $m/6$ remains stationary,find the velocity of the other part.

$A$ bullet of mass $m$ moving with velocity $v$ is fired into a wooden block of mass $M$. If the bullet remains embedded in the block,the final velocity of the system is:

$A$ bomb moving with velocity $(40 \hat{i} + 50 \hat{j} - 25 \hat{k}) \text{ m/s}$ explodes into two pieces of mass ratio $1:4$. After the explosion,the smaller piece moves away with velocity $(200 \hat{i} + 70 \hat{j} + 15 \hat{k}) \text{ m/s}$. The velocity of the larger piece after the explosion is:

You are on a frictionless horizontal plane. How can you get off if no horizontal force is exerted by pushing against the surface?

$A$ man (mass $= 50\, kg$) and his son (mass $= 20\, kg$) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of $0.70\, ms^{-1}$ with respect to the man. The speed of the man with respect to the surface is ........ $ms^{-1}$

$A$ body of mass $5 \ kg$ initially at rest explodes into three fragments. The ratio of the masses of the three fragments is $1 : 1 : 3$. The two fragments of equal mass move in mutually perpendicular directions with a velocity of $21 \ m/s$. What is the velocity of the heaviest fragment in $m/s$?