The GATE Grind

GATE 2016 ME (ME2) – Question 16

Engineering Mechanics · Impulse and momentum, energy formulations · 1 mark · Multiple choice

A point mass having mass M is moving with a velocity V at an angle θ 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

Diagram for GATE 2016 ME (ME2) question 16
  1. $-2MV\cos\theta\,\hat j$
  2. $2MV\sin\theta\,\hat j$
  3. $2MV\cos\theta\,\hat j$
  4. $-2MV\sin\theta\,\hat j$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) $-2MV\sin\theta\,\hat j$

Explanation

The wall is horizontal, so tangential x velocity is unchanged. The upward normal component Vsinθ reverses to−Vsinθ in a perfectly elastic collision. Therefore final minus initial momentum is **−2MVsinθ in the j direction, D**. Smoothness excludes tangential impulse.