Question

A ball of mass $m$ collides with a stationary identical ball with a speed $v_0$. Find the impulse of the colliding balls. $(e=1/2)$

• A. $5/4m{v}_0$
• B. $3/4m{v}_0$
• C. $4/4m{v}_0$
• D. $9/4m{v}_0$

Answer 1

Answer: (B)

$3/4m{v}_0$

R.E.F image

By conservation of momentum

$m{v}_0=m{v}_1+m{v}_2\Rightarrow v_0=v_1+v_2...\left(1\right)$

$e=\frac{velocityofseparation}{velocityofapproach}\Rightarrow \frac{v_2-v_1}{v_0-0}=\frac{1}{2}$

$\Rightarrow v_2-v_1=\frac{v_0}{2}...\left(2\right)$

$\left(1\right)+\left(2\right)\Rightarrow 2v_2=\frac{3v_0}{2}\Rightarrow v_2=\frac{3v_0}{4}$

We know that impulse $=$ change in momentum

$\Rightarrow$ impulse $=m{v}_2-0=\frac{3m{v}_0}{4}$

Therefore option B is correct