PYQ NEET- Problem Solving Newton’S Second Law

2016 Q1:

The answer is (C).

The momentum of the first particle is $mv_0$. The momentum of the second particle is $0$. After the collision, the momentum of the first particle is $\frac{mv_0}{3}$. The momentum of the second particle is $2mv_0$. The total momentum is conserved, so $mv_0 + 0 = \frac{mv_0}{3} + 2mv_0$. This gives $0 = \frac{2mv_0}{3}$.

Q2:

The answer is (C).

The kinetic energy of the bullet is $\frac{1}{2}mv^2$. The kinetic, energy of the block is $\frac{1}{2}Mv^2$. The total kinetic energy is $\frac{1}{2}mv^2 + \frac{1}{2}Mv^2 = \frac{v^2(m + M)}{2}$