A particle of mass M initially at rest splits into two. If one of the particles of mass M1 moves with velocity V1 , the second particle moves with velocity

Analyze the question: A body of mass M, initially at rest, splits into two parts. We need the velocity of the second part. This is a conservation of linear momentum problem.

Concept: With no external force, total momentum is conserved. The momentum before the split is zero because the body is at rest.

Solution:

Momentum before = 0

The second particle has mass M₂ = M − M1 and velocity V₂.

Momentum after = M1V1 + (M − M1)V₂

Setting momentum before equal to momentum after:

0 = M1V1 + (M − M1)V₂

(M − M1)V₂ = −M1V1

V₂ = −M1V1 / (M − M1)

Writing the denominator the other way round:

V₂ = M1V1 / (M1 − M)

Interpreting the result: The negative sign shows the second particle moves in the opposite direction to the first, as expected. Its magnitude is M1V1/(M − M1).

Checking the options:

• A: M1V1/(M − M1) gives the correct magnitude but has no negative sign, so it does not show the opposite direction.
• B: M1V1/(M1 − M) is exactly our result, with the negative sign built into the denominator.
• C: M1V1/M is wrong because it ignores that the second mass is M − M1.
• D: uses MV, which is not defined in the problem.

Tip: For "at rest then splits or explodes" questions, always start with 0 = m₁v₁ + m₂v₂. The two parts always move in opposite directions, so look for the option with the negative sign, which may be hidden in a reversed denominator like (M1 − M).