# A Ball of Mass M is Dropped onto a Floor from a Certain Height. the Collision is Perfectly Elastic and the Ball Rebounds to the Same Height and Again Falls. - Physics

Sum

A ball of mass m is dropped onto a floor from a certain height. The collision is perfectly elastic and the ball rebounds to the same height and again falls. Find the average force exerted by the ball on the floor during a long time interval.

#### Solution

It is given that the mass of the ball is m.

Let the ball be dropped from a height h.

The speed of ball before the collision is v1.
$\therefore \text{v}_1 = \sqrt{2\text{gh}}$
The speed of ball after the collision is v2.
$\text{v}_2 = - \sqrt{2\text{gh}}$
$\text{ Rate of change of velocity = acceleration }$
$\Rightarrow a = \frac{2\sqrt{2gh}}{t}$
$\therefore \text{ Force}, F = \frac{m \times 2\sqrt{2gh}}{t} \ldots(1)$
Using Newton's laws of motion, we can write:
$v = \sqrt{2gh}, s = h, u = 0$
$\Rightarrow \sqrt{2gh} = gt$
$\Rightarrow t = \sqrt{\frac{2h}{g}}$
$\therefore \text{ Total time }= 2\sqrt{\frac{2h}{g}}$
Substituting this value of time t in equation (1), we get:
F  = mg

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#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 9 Centre of Mass, Linear Momentum, Collision
Q 25 | Page 161