Question

Two perfectly elastic balls of the same mass $m$ are moving with velocities $u_1$ and $u_2$. They collide head on elastically, $n$ times. The kinetic energy of the sytem 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

The correct option is C $\frac{1}{2}m(u_1^2+u_2^2)$

As we know,
In elastic collision kinetic energy of the system remains same before and after the collision.
Hence after the collision, $KE$ will be same as the initial kinetic energy before the collision.
Therefore, kinetic energy after $n$ collisions$=\frac{1}{2}m{u}_1^2+\frac{1}{2}m{u}_2^2=\frac{1}{2}m(u_1^2+u_2^2)$