Two rings of mass m and 2 m 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 i

Question

Two rings of mass m and 2 m 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

TestHub · Accepted Answer

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,

$\frac{1}{2} k x_{m a x}^{2} = \frac{1}{2} μ v_{0}^{2} [μ = R e d u c e d m a s s]$

$\Rightarrow x_{m a x} = \sqrt{\frac{μ}{k}} . v_{0} = \sqrt{\frac{2 m}{3 k}} v_{0}$

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