GATE ME 2023 Set 1 — Question 37
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Engineering Mechanics → Dynamics → Linear & Angular Impulse-Momentum
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Question
A spherical ball weighing 2 kg is dropped from a height of 4.9 m onto an immovable rigid block as shown in the figure. If the collision is perfectly elastic, what is the momentum vector of the ball (in kg m/s) just after impact?Take the acceleration due to gravity to be . Options have been rounded off to one decimal place.

Correct answer
(C) 17.0 i + 9.8 j
Solution
1.Velocity of the ball just before impact: . The velocity vector is .
2.Momentum just before impact: .
3.The surface is inclined at to the horizontal. The unit normal vector to the surface (pointing outwards) is .
4.For a perfectly elastic collision with an immovable object, the momentum after impact is given by:
5.Calculate the dot product: .
6.Substitute back:
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