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Question

A ball is dropped vertically from height h and is bouncing elastically on the floor (see figure). Which of the following plots best depicts the acceleration of the ball as a function of time.
738272_ab1c607d6d09492fb3fa9da389672014.png
  1. 738272_2505792_08a6c921648a4b6ca8cf61167cdd8476.png
  2. 738272_2505793_ed39dfe5ed9b4675b62fc52525159fe1.png
  3. 738272_2505794_4542e9cec9a149c5ad849e31c4e52247.png
  4. 738272_2505795_99963c744a094bb79d2c5b5af2957279.png

A
738272_2505792_08a6c921648a4b6ca8cf61167cdd8476.png
B
738272_2505794_4542e9cec9a149c5ad849e31c4e52247.png
C
738272_2505793_ed39dfe5ed9b4675b62fc52525159fe1.png
D
738272_2505795_99963c744a094bb79d2c5b5af2957279.png
Solution
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During free fall of the ball, gravitational force acts on the body in downward direction always and so the acceleration of the ball remains in vertically downward direction which is constant with time. Its acceleration becomes positive only at single instant of time during the collision of ball with the ground. The ground imparts an upward impulse and hence the upward acceleration on the ball which makes the ball to move upward, but as soon as the ball looses contact with the ground, its accelerates in the downward direction again. Hence, option B is correct.

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