Question

Particle A of mass m experiences a perfectly elastic collision with a stationary particle B of mass M. After the collision (head-on) the particles fly apart in opposite directions with equal velocities. Then:

• A. $\frac{m}{M}=1$
• B. $\frac{m}{M}=3$
• C. $\frac{m}{M}=2$
• D. $\frac{m}{M}=\frac{1}{3}$

Answer 1

The correct option is D $\frac{m}{M}=\frac{1}{3}$


$\underset{–}{COM}$
$mu=-mv+Mv$
$\Rightarrow v=\frac{mu}{M-m}...\left(1\right)$
$\underset{–}{NLC}$
$v_2-v_1=e(U_1-U_2)$
$v-(-v)=\left(1\right)(v-0)$
$2v=v....\left(2\right)$
$\left(2\right)in\left(1\right)$
$\frac{u}{2}=\frac{mu}{M-m}$
$\Rightarrow 3m=M$
$\frac{m}{M}=\frac{1}{3}$