Question

Two rings of mass $m$ and $2m$ are connected with a massless spring and can slip over two frictionless parallel horizontal rails having separation equal to the unstretched length of the spring as shown in figure. Ring of mass $m$ is given velocity $v_0$ in the direction shown. Maximum length by which the spring will be stretched is

• A. $\sqrt{\frac{m}{k}}{v}_0$
• B. $\sqrt{\frac{3m}{k}}{v}_0$
• C. $\sqrt{\frac{2m}{3k}}{v}_0$
• D. $\sqrt{\frac{2m}{k}}{v}_0$

Answer 1

Answer: (C)

Maximum expansion takes place only when both the rings move with the same speed.
Therefore we can apply work-energy theorem here. So maximum expansion in spring is obtained by,
$\frac{1}{2}k{x}_{max}^2=\frac{1}{2}\mu v_0^2\left[\mu =Reducedmass\right]$
$\Rightarrow x_{max}=\sqrt{\frac{\mu }{k}}.v_0=\sqrt{\frac{2m}{3k}}{v}_0$