A 0.5 kg ball moving with a speed of 12 m/s strikes a hand wall at an angle of 30 o with the wall. It is reflected with the same speed at the same angle. If the ball is in contact with the wall for 0.25 seconds, the average force acting on the wall is :

Center of Mass and Collision PYQ — NEET 2006 · Q157 with Solution

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Correct answer: C

AIPMT 2006 Physics - Center of Mass and Collision Question 35 English Explanation 1

Resolving the velocities in vertical and horizontal directions, resolved parts of first velocity

AIPMT 2006 Physics - Center of Mass and Collision Question 35 English Explanation 2

v cos$\theta $ perpendicular to the wall and v sinq parallel to the wall. In the second case, they are –v sin$\theta $ & v cos$\theta $ respectively. Here, –ve sign is because direction is opposite to the earlier ones. So we see a net change in velocity perpendicular to way
= v sin$\theta $ – (–v sin$\theta $) = 2v sin$\theta $

This change has occured in 0.25 sec, so, rate of

change of velocity = $${{2v\sin \theta } \over {0.25}}$$

$$ = {{2 \times 12 \times \sin 30^\circ } \over {0.25}} \Rightarrow {{24 \times 1} \over {2 \times 0.25}} = 48$$

Thus, acceleration a = 48 m/sec²

Force applied = m $ \times $ a = 0.5 × 48 = 24 N

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