Question

In the figure shown, a spring mass system is placed on a horizontal smooth surface in between two vertical rigid walls $W_1$ and $W_2$. One end of spring is fixed with wall $W_1$ and other end is attached with mass $m$ which is free to move. Initially, spring is tension free and having natural length $l_0$. Mass $m$ is compressed through a distance a and released. Taking the collision between wall $W_2$ and mass $m$ as elastic and $K$ as spring constant, the average force exerted by mass $m$ on wall $W_2$ in one oscillation of block is

• A. $\frac{2aK}{\pi }$
• B. $\frac{2ma}{\pi }$
• C. $\frac{aK}{\pi }$
• D. $\frac{2aK}{m}$

Answer 1

The correct option is A $\frac{2aK}{\pi }$

maximum velocity $v_{max}=\omega A\left(\sqrt{\frac{K}{m}}\right)a$
Change in momentum $\Delta P=2m{v}_{max}=2m\left(\sqrt{\frac{K}{m}}\right)a$
Force exerted by the mass$m$ on wall $W_2$ is $F=\frac{\Delta P}{\Delta t}=\frac{\Delta P}{T/2}=\frac{2ma\sqrt{k/m}}{\pi \sqrt{m/k}}=\frac{2aK}{\pi }$