Question

A tennis ball is dropped on a horizontal smooth surface. It bounces back after hitting the surface. The force on the ball during the collision is proportional to the degree 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 scale.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B


Initially $u=0$.
Velocity of ball at time $t$ before hitting the surface will be given by:
$v=u+at$ where $a=+g$ taking downwards as +ve direction
$\therefore v=gt....\left(i\right)$
Kinetic energy of the ball at time $t$ before striking surface,
$KE=\frac{1}{2}m{v}^2$
From Eq. $\left(i\right)$
$KE=\frac{1}{2}m{g}^2{t}^2$
$\because m\&g$ are constant
$\Rightarrow KE\propto t^2$
$\therefore$ We will get an upward parabola before the ball hits the surface.

When the ball hits the surface, it will have some kinetic energy. Its kinetic energy $K$ will start to transform into elastic potential energy as it will be deformed more and more after increased compression till $KE=0$ at maximum deformation. It will try to regain its shape (due to elasticity of material) after maximum deformation is achieved. Hence once again, $KE$ begins to increase from $\text{zero}$. These transitions of $KE$ take place instantaneously, as impulsive forces are very short interval forces.

When ball starts rising upwards after striking the surface, its $KE$ will decrease owing to the retardation caused by gravity. This will give a downward parabola.
$\therefore$ Option $\left(b\right)$ represents the best possible graph.