Question

A ball of mass $m$ moving with speed $v_0$ bounces back and forth between two massive stationary walls separated by a distance $\ell$. The collisions are perfectly elastic and effect of gravity is to be neglected. One of the walls starts moving slowly towards the other wall with speed $v_1(v_1\ll <v_0)$ find the velocity of ball when the distance between the walls has been reduced $\ell /2$ to (Assume mass of wall $>>m$

• A. data insufficient
• B. $v_0$
• C. $2v_0$
• D. $v_0+2v_1$

Answer 1

The correct option is C $2v_0$

During each collision with wall $A$, velocity of the ball increases by $2v_1$ but velocity of wall remains unchanged.
$\frac{2x}{v}=\frac{(-\Delta x)}{v_1}\text{but}\Delta v=2v_1$
$\frac{-\Delta x}{\Delta v}=\frac{x}{v};$
or $k-{\int }_{\ell }^{\ell /2}\frac{dx}{x}={\int }_{v_0}^v\frac{dv}{v}\to v=2v_0$
Final Answer: (c)