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

Solution

Physics sir · 4 steps

The nucleus starts at rest, so the two pieces must carry equal and opposite momenta.

1. Momentum before. The nucleus is at rest, so the total momentum is zero. Only internal forces act during the break-up, so the total momentum stays zero afterwards.

   0 = m₁ v⃗₁ + m₂ v⃗₂ ⇒ m₁ v⃗₁ = - m₂ v⃗₂

2. Direction. The minus sign means the two velocities point in opposite directions. The momentum magnitudes are equal: m₁ v₁ = m₂ v₂.
3. Speed ratio. Take m₁ : m₂ = 2 : 1. Then v₁/v₂ = m₂/m₁ = 1/2, so the heavier piece moves at half the speed of the lighter one.
4. So. The nuclei move in opposite directions with speeds in the ratio 1 : 2, which is option (a).

The idea to keep. When something at rest splits into two, the pieces fly apart with equal and opposite momenta. Speed goes as the inverse of mass: the heavier piece moves slower.

Answer from the NTA final answer key. Solution by PrepWiser.