Two identical balls are suspended side by side by two long strings. One ball is pulled aside so that its center of gravity rises by a vertical distance $h$. It is then released and undergoes a perfectly inelastic collision with the other ball. What is the vertical distance to which the center of gravity of the combined system rises?

Two bodies $A$ and $B$ of same mass undergo a completely inelastic one-dimensional collision. The body $A$ moves with velocity $v_1$ while body $B$ is at rest before the collision. The velocity of the system after the collision is $v_2$. The ratio $v_1: v_2$ is

$A$ bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be

$A$ neutron of mass $1.67 \times 10^{-27} \ kg$ moving with a velocity of $10^8 \ m/s$ collides with a deuteron at rest and sticks to it. If the mass of the deuteron is $3.34 \times 10^{-27} \ kg$,what will be the velocity of the combined system?

Two identical blocks of ice move in opposite directions with equal speed and collide with each other. What will be the minimum speed required to make both the blocks melt completely, if the initial temperatures of the blocks were $-8^{\circ} C$ each (in $ms^{-1}$)? (Specific heat of ice is $2100 \ Jkg^{-1} K^{-1}$ and latent heat of fusion of ice is $3.36 \times 10^{5} \ Jkg^{-1}$)

$A$ bullet of mass $m$ and velocity $v$ when fired at a sand bag of mass $M$,suspended by a string,gets embedded into the bag. The loss of kinetic energy in this process is