Determine what will happen to the momentum of an object if the velocity is doubled and mass is halved. (K:1)

Question

BlackTom AI · Accepted Answer

The problem asks what happens to the momentum when velocity is doubled and mass is halved. Momentum is defined as p = m v, so we should compare the initial momentum to the final momentum after applying the changes.
Option a: 'It does not change' — Calculate the new momentum: p' = (m/2) * (2v) = m v = p. The two changes cancel each other, leaving the momentum unchanged. This matches the correct reasoning.
Option b: 'It becomes 4 times the original momentum' — If momentum were to quadruple, p' would have to equal 4 p. However, the calculation shows p' = p, so this is incorrect.
Option c: 'It becomes two times the original momentum' — Doubling the momentum would require p' = 2 p. But since p' = p, this option misstates the effect of the combined changes and is false.
Option d: 'It becomes half of the original momentum' — Halving the momentum would mean p' = p/2. The actual result from p' = (m/2)(2v) is p, not p/2, so this is incorrect.
In summary, the key idea is that momentum depends linearly on both mass and velocity, and when one increases (velocity doubles) while the other decreases (mass halves) by the same factor, the product m v remains unchanged. The math p' = (m/2) * (2v) simplifies to p, confirming that the final momentum equals the initial momentum.

Determine what will happen to the momentum of an object if the velocity is doubled and mass is halved. (K:1)

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