Question

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2:1. After disintegration they will move

• A. In opposite directions with speed in the ratio of 1:2 respectively
• B. In opposite directions with speed in the ratio of 2:1 respectively
• C. In the same direction with same speed.
• D. In opposite directions with the same speed.

Answer 1

Answer: (A)

In opposite directions with speed in the ratio of 1:2 respectively

Answer 2

Since the nucleus is at rest before disintegration, the total momentum of the system is zero. By the law of conservation of momentum, the momentum after disintegration must also be zero. The two smaller nuclei move in opposite directions, and the speed ratio is inversely proportional to their mass ratio.

Let the masses of the two nuclei be $m_1 = 2m$ and $m_2 = m$, and their speeds be $v_1$ and $v_2$, respectively. Using conservation of momentum:

$m_1 v_1 + m_2 v_2 = 0 \implies 2m \cdot v_1 + m \cdot v_2 = 0 \implies v_2 = -2v_1$

Thus, the speed ratio is $1 : 2$, and they move in opposite directions.