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Question

A nucleus moving with a velocity v emits an α-particle. Let the velocities of the α-particle and the remaining nucleus be v1 and v2 and their masses be m1 and m2.
(a) v,v1 and v2 must be parallel to each other.
(b) None of the two of v,v1 and v2 should be parallel to each other.
(c) v1+v2 must be parallel to v
(d) m1v1+m2v2 must be parallel to v

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Solution

(d) m1v1+m2v2 must be parallel to v

By the law of conservation of linear momentum, we can write:

Initial momentum = Final momentummv = m1v1 + m2v2(m1v1 + m2v2) must be parallel to v

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