JEE Physics 2023 Question with Solution

Given: First particle has mass $m$ and velocity $v$. Second particle has mass $2m$ and is at rest.

Find: The common velocity after collision when both particles stick together.

Since the particles stick together, this is a perfectly inelastic collision. Use conservation of linear momentum.

Initial momentum:

$$p_i = m_1 v_1 + m_2 v_2 = mv + 0 = mv$$

Combined mass after collision:

$$m_{\text{combined}} = m + 2m = 3m$$

Let the final common velocity be $V$. Then final momentum is:

$$p_f = (3m)V$$

By conservation of momentum:

$$p_i = p_f$$

So,

$$mv = 3mV$$

Hence,

$$V = \frac{v}{3}$$

Therefore, the final velocity is $\frac{v}{3}$. The correct option is B.

The solution labels the option as C, but the working clearly gives $\frac{v}{3}$, which matches option B in the provided options.