Question

A metal ball falls from a height of $1\text{m}$ on a steel plate and jumps upto a height of $81\text{cm}$. Find the coefficient of restitution for the collision.

• A. $0.7$
• B. $0.8$
• C. $0.6$
• D. $0.9$

Answer 1

The correct option is D $0.9$

Let,
$u_1=$ Speed of ball before collision with surface
$v_1=$ Speed of ball after collision with surface
$u_2=$ Speed of plate before collision$=0$
$v_2=$ Speed of plate after collision $=0$
The coefficient of restitution, $e=\frac{\text{speed of separation}}{\text{speed of approach}}$

Speed of separation = $v_1-v_2=v_1...i$
Speed of approach=$u_1-u_2=u_1...ii$

$\therefore e=\frac{v_1}{u_1}....iii$
Since ball is dropped from height $1\text{m}$, it's speed while just colliding with plate is :
$u_1=\sqrt{2gh}=\sqrt{2\times 10\times 1}=\sqrt{20}$

using, $v^2=u^2+2as$
$v=u^2-2gh$
Taking upwards=$+ve,v=0,u=v_1,a=-g,s=+h=0.81\text{m}$
$\Rightarrow 0=v_1^2-2(10\times 0.81)$
$\therefore v_1=\sqrt{2\times 10\times 0.81}$

From Eq. $\left(iii\right)$

$\Rightarrow e=\frac{\sqrt{2\times 10\times 0.81}}{\sqrt{20}}=\sqrt{0.81}$
$\therefore e=0.9$