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 bullet of mass $50$ gram is fired from a $5 \,kg$ gun with a velocity of $1km/s$. the speed of recoil of the gun is .......... $m/s$

A shell of mass $m$ moving with velocity $v$ suddenly breaks into $2$ pieces. The part having mass $m/3$ remains stationary. The velocity of other part will be

Two skaters $A$ and $B$ of weights in the ratio $5 : 7$ start facing each other $6\,metres$ apart on a horizontal smooth surface. They pull on a rope stretched between them. How far has each moved when they meet?

A spring is compressed between two toy carts of mass $m_1$ and $m_2$. When the toy carts are released, the springs exert equal and opposite average forces for the same time on each toy cart. If $v_1$ and $v_2$ are the velocities of the toy carts and there is no friction between the toy carts and the ground, then :

An object of mass $3\,m$ splits into three equal fragments. Two fragments have velocities $v\hat j$ and $v\hat i$. The velocity of the third fragment is