Question

The coefficient of restitution for collision between the ball and the block is:

• A. $0.50$
• B. $0.75$
• C. $1.0$
• D. $0.30$

Answer 1

The correct option is C $1.0$

Given, take $g=10m/s^2$

$m=1kg$ both have same mass

$\theta ={60}^0$

$l=2.50m$

$x=2.5m$ block moves after collision

Lets consider the speed of ball is $u_1$ which collide with the collision with block at rest. and the velocity of ball and block after collision is $v_1$ and $v_2$ respectively.

The potential energy loss by the ball=Kinetic energy of block

$mgH=\frac{1}{2}m{u}_1^2$ . . . .. .(1)

In image,

$H=1.25m$

$u_1=5m/s$ (by putting the value of $H$ in equation 1)

The coefficient of restitution

$e=$relative velocity after collision/ relative velocity before collision

Work done by the friction is

$\mu mg=\frac{1}{2}m{v}_2^2$

$v_2=\sqrt{2\mu g}$......(2)

and lets the velocity of ball after collision is $v_3$.

so, $e{u}_1=(5-v_2)$. . . . . .(3)

By the conservation of momentum,

$m_1{u}_1+m_1{u}_1=m_1{v}_1+m_2{v}_2$

$u_1=v_1+v_2$

$v_2=5-\sqrt{2\mu g}=0m/s$, the friction coefficient is less than 1.

From equation (3), we get,

$e=1$

The correct option is A.