A bomb of mass 16 kg at rest explodes into two pieces of masses of 4 kg and 12 kg. The velocity of the 12 kg mass is $4$ ms$^{-1}$. The kinetic energy of the other mass is
(1) 96 J
(2) 144 J
(3) 288 J
(4) 192 J

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 ball of mass 10 kg moving with a velocity $10 \sqrt { 3 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$ along the $x$-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along $y$-axis with a speed of $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The second piece starts moving at an angle of $30 ^ { \circ }$ with respect to the $x$-axis. The velocity of the ball moving at $30 ^ { \circ }$ with $x$-axis is $x \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The configuration of pieces after the collision is shown in the figure below. The value of $x$ to the nearest integer is [Figure]

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) $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$