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

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, m k v 0, 3 m k v 0, 2 m 3 k v 0, 2 m k v 0

MARKS App · 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, 1 2 k x m a x 2 = 1 2 μ v 0 2 μ = R e d u c e d m a s s ⇒ x m a x = μ k . v 0 = 2 m 3 k v 0

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