A spring is compressed between two blocks of masses $m_{1}$ and $m_{2}$ placed on a horizontal frictionless surface as shown in the figure. When the blocks are released, they have initial velocity of $v_{1}$ and $v_{2}$ as shown. The blocks travel distances $x_{1}$ and $x_{2}$ respectively before coming to rest. The ratio $\left(\frac{x_{1}}{x_{2}}\right)$ is
(1) $\frac{m_{2}}{m_{1}}$
(2) $\frac{m_{1}}{m_{2}}$
(3) $\sqrt{\frac{m_{2}}{m_{1}}}$
(4) $\sqrt{\frac{m_{1}}{m_{2}}}$

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 $0.70 \text{ m s}^{-1}$ with respect to the man. The speed of the man with respect to the surface is:
(1) $0.20 \text{ m s}^{-1}$
(2) $0.14 \text{ m s}^{-1}$
(3) $0.47 \text{ m s}^{-1}$
(4) $0.28 \text{ m s}^{-1}$

A body of mass $M$ at rest explodes into three pieces, in the ratio of masses $1 : 1 : 2$. Two smaller pieces fly off perpendicular to each other with velocities of $30 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $40 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ respectively. The velocity of the third piece will be
(1) $35 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $50 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$