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 the same direction with same speed. (c) in opposite directions with speed in the ratio of 2: 1 respectively. (d) in opposite directions with the same speed.

Answer: (a). Initial momentum is zero, so m₁ v₁ = m₂ v₂ and the parts move in opposite directions. (v₁)/(v₂) = (m₂)/(m₁) = 1/2 So the answer is (a) opposite directions with speeds in the ratio 1: 2.

A nucleus at rest disintegrates into two smaller nuclei with their… | JEE Main 2024 (9 Apr, Shift 2)

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Nuclear Reactions & Q-value

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

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Answer: (a)

Initial momentum is zero, so $m_1 v_1 = m_2 v_2$ and the parts move in opposite directions.
$\dfrac{v_1}{v_2} = \dfrac{m_2}{m_1} = \dfrac{1}{2}$
So the answer is (a) opposite directions with speeds in the ratio $1 : 2$ .

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