Question

Two perfectly elastic balls of same mass m are moving with velocities $u_{1}and{u}_2$. They collide head on elastically n times. The kinetic energy of the system finally is :

• A. $\frac{1}{2}\frac{m}{n}{u}_1^2$
• B. $\frac{1}{2}\frac{m}{n}(u_1^2+u_2^2)$
• C. $\frac{1}{2}m(u_1^2+u_2^2)$
• D. $\frac{1}{2}mn(u_1^2+u_2^2)$

Answer 1

Answer: (C)

$\frac{1}{2}m(u_1^2+u_2^2)$

Under all collisions momentum is conserved.
Under elastic collisions, even Kinetic energy is conserved.
So the final KE after 'n' collisions would be the same as the initial.
$KE=\frac{1}{2}\left(m\right)(u_1^2+u_2^2)$
Option C is correct.