GATE ME 2016 Set 2 — Question 16
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Engineering Mechanics → Dynamics → Linear & Angular Impulse-Momentum
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Question
A point mass having mass is moving with a velocity at an angle to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth wall and rebounds. The total change (final minus initial) in the momentum of the mass is
Correct answer
(D) -2MV sin θ j
Solution
Let the wall be along the -axis. The initial velocity vector is .
Since the wall is smooth and the collision is perfectly elastic, the component of velocity parallel to the wall (-component) remains unchanged, while the component normal to the wall (-component) reverses its direction.
Final velocity vector: .
Change in momentum :
.
Since the wall is smooth and the collision is perfectly elastic, the component of velocity parallel to the wall (-component) remains unchanged, while the component normal to the wall (-component) reverses its direction.
Final velocity vector: .
Change in momentum :
.
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