JEE Physics 2024 Question with Solution

Given: A nucleus is initially at rest, so the initial momentum of the system is $0$. The two smaller nuclei have masses in the ratio $2:1$.

Find: The direction of motion and the ratio of their speeds after disintegration.

Use the conservation of momentum. Since no external force acts on the system, total momentum remains constant.

Let the masses of the two smaller nuclei be $m_1 = 2m$ and $m_2 = m$. Let their speeds be $v_1$ and $v_2$ respectively. Because the initial momentum is zero, after disintegration the two nuclei must move in opposite directions so that their momenta cancel.

Applying conservation of momentum:

So,

Cancelling $m$,

Hence,

Given: The parent nucleus is at rest, so total initial momentum is $0$. The daughter nuclei have mass ratio $2:1$.

Find: Their speed ratio and direction after disintegration.

For a system initially at rest, the two fragments produced must have equal and opposite momenta:

Thus, speed is inversely proportional to mass.

Since $m_1 : m_2 = 2 : 1$,

The two nuclei move in opposite directions.

Therefore, the correct option is A.