$A$ spring is compressed between two toy carts of mass $m_1$ and $m_2$. When the toy carts are released,the spring exerts 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 :

In an explosion,a body breaks up into two pieces of unequal masses. In this process:

$A$ ball of mass $200\,g$ rests on a vertical post of height $20\,m$. $A$ bullet of mass $10\,g$,travelling in a horizontal direction,hits the centre of the ball. After the collision,both travel independently. The ball hits the ground at a distance of $30\,m$ and the bullet at a distance of $120\,m$ from the foot of the post. The value of the initial velocity of the bullet will be $............m/s$ (if $g = 10\,m/s^2$).

$A$ rifleman,who together with his rifle has a mass of $100\,kg$,stands on a smooth surface and fires $10$ shots horizontally. Each bullet has a mass of $10\,g$ and a muzzle velocity of $800\,ms^{-1}$. The velocity which the rifleman attains after firing $10$ shots is $..........\,ms^{-1}$.

$A$ bomb of mass $12\,kg$ at rest explodes into two fragments of masses in the ratio $1 : 3$. The $K.E.$ of the smaller fragment is $216\,J$. The momentum of the heavier fragment is (in $kg\cdot m/s$):

$A$ bullet of mass $10\, g$ is fired from a gun of mass $1\, kg$. If the recoil velocity of the gun is $5\, m/s$,the muzzle velocity of the bullet is ........ $m/s$.