$A$ bullet of mass $a$ moving with velocity $b$ strikes a block of mass $c$ and gets embedded in it. Find the velocity of the block.

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 $m$ travelling with a speed $v$ hits a block of mass $M$ initially at rest and gets embedded in it. The combined system is free to move and there is no other force acting on the system. The heat generated in the process will be

$A$ neutron having a mass of $1.67 \times 10^{-27} \ kg$ and moving at $10^8 \ m/s$ collides with a deuteron at rest and sticks to it. If the mass of the deuteron is $3.34 \times 10^{-27} \ kg$,then the speed of the combination is:

$A$ body of mass $5\,kg$ strikes another body of mass $2.5\,kg$ initially at rest. The bodies after collision coalesce and begin to move as a whole with a kinetic energy of $5\,J$. The kinetic energy of the first body before collision is ............... $J$.

Find the correct option based on the two statements given below.
Statement-$1$ : Two particles moving in the same direction do not lose all their energy in a perfectly inelastic collision.
Statement-$2$ : The law of conservation of linear momentum is obeyed for all types of collisions.