Centre of Mass 4 Question 1
2. A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy $K$ with time $t$ most appropriately? The figures are only illustrative and not to the scale.
(2014 Adv.) (a)
(c)
(b)
(d)
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Answer:
Correct Answer: 2. (b)
Solution:
$$ \begin{gathered} t=0 \bullet \\ \text { (Before collision) } \prod _{V=g t} \\ K=\frac{1}{2} m g^{2} t^{2} \\ K \propto t^{2} \text { Therefore, } K-t \text { graph is parabola. } \end{gathered} $$
During collision, retarding force is just like the spring force $(F \propto x)$, therefore kinetic energy first decreases to elastic potential energy and then increases.
