JEE Advance - Physics (2014 - Paper 2 Offline - No. 5)
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.
Maelezo
As tennis ball is dropped, so its initial velocity, u = 0
Suppose its velocity at any time t = v
Acceleration due to gravity = g
$$\therefore$$ v = u + gt
$$\Rightarrow$$ v = gt ..... (i)
We know, kinetic energy,
$$K = {1 \over 2}m{v^2} = {1 \over 2}m({g^2}{t^2})$$ [Using eqn. (i)]
$$ \Rightarrow K = {1 \over 2}m{g^2}{t^2}$$
$$ \Rightarrow K \propto {t^2}$$ (As m and g are constant)
This shows that relation between kinetic energy of tennis ball K and time t is parabolic.
During the collision, velocity of the ball falls sharply to zero as it is compressed and regains maximum velocity in the same short time interval.
This relation is best illustrated by the option (b).