Question

A 90gm ball moving at 100 cm/s collide head on with a stationary 10gm ball. The coefficient of restitution is 0.5 . Their respective velocities after collision are

• A. 135 cm/s, 85 cm/s
• B. 85 cm/s, 135 cm/s
• C. -85 cm/s, 135 cm/s
• D. 85 cm/s,-135 cm/s

Answer 1

Answer: (B)

85 cm/s, 135 cm/s

Let
$m_1=$Mass of moving body$=90$gm
$m_2=$Mass of stationary body$=10$gm
$u_1=$Velocity of first body before collision$=100$cm/s
$u_2=$Velocity of second body before collidion$=0$cm/s
$v_1$ and $v_2$ are velocities after collision.
Using momentum conservation,

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

$\Rightarrow 90\times 100+10\times 0=90\times v_1+10\times v_2$

$\Rightarrow 9v_1+v_2=900$...............(1)

Using equation for coefficient for restitution,

$e=-\frac{v_1-v_2}{u_1-u_2}$

$\frac{1}{2}=-\frac{v_1-v_2}{u_1-u_2}=\frac{v_2-v_1}{100}$

$\Rightarrow v_2-v_1=50$..............(2)
Solving the equations(1) and (2), $v_1=135$cm/s$,v_2=85$cm/s