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Two billiard balls of equal mass 30 g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball a and ball b by the wall along X direction is

Asked in JEE Main 25th July 1st Shift 2021 · Bounces, catches and repeated impacts

Figure: Bounces, catches and repeated impacts
Answer: (1) √2:1

Step-by-step solution

Idea: the wall is smooth, so only the component of velocity perpendicular to the wall reverses. Resolve along X and compare.

Both balls arrive at the same speed u and leave at the same speed.

Ball a, head-on: its whole velocity is along X and it reverses, so

|Jₐ|=2mu.

Ball b, at 45°: only u cos 45° lies along X, and only that reverses, so

|J_b|=2mu cos 45°=(2mu)/(√2).

(|Jₐ|)/(|J_b|)=(2mu)/(2mu/√2)=√2, so the ratio is √2:1.

Neither the mass nor the 108 kmph is needed: both cancel in the ratio, and the answer would be the same for any common speed.

Why the other options are wrong

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