When a nucleus at rest spontaneously splits into fragments of mass m₁ and m₂, the ratio of the velocity of m₁ to the velocity of m₂ is A) . B) . C) −1. D) . E) .

Question

Quizplus · Accepted Answer

The conservation of momentum and conservation of energy laws can be applied to solve this problem. The mass of the nucleus before and after the split is the same, so the momentum before and after the split must also be the same. Since the velocity of the nucleus is zero before the split, the total momentum before the split is zero. Therefore, the total momentum after the split must be zero as well. Let the velocity of the fragment with mass m₁ be v1 and the velocity of the fragment with mass m₂ be v2. Then we have: m₁v1 + m₂v2 = 0 Solving for v1/v2, we get: v1/v2 = -m₂/m₁ Since the masses of the fragments are not given, we cannot compute the exact value of v1/v2. However, we can see from the equation that v1/v2 is negative, which means the velocity of fragment 1 (m₁) is in the opposite direction to the velocity of fragment 2 (m₂). The only answer choice that satisfies this condition is B.

When a Nucleus at Rest Spontaneously Splits into Fragments of Mass