Two ring of mass m and 2m are connected with a light spring and can slide over two frictionless parallel horizontal rails as shown in figure. Ring of mass m is given velocity ‘v₀’ in horizontal direction as shown. Calculate the maximum stretch in spring during subsequent motion.

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$\sqrt{\frac{3 m}{2 k}} v_{0}$

$\sqrt{\frac{2 m}{3 k}} v_{0}$

$\sqrt{\frac{m}{3 k}} v_{0}$

$\sqrt{\frac{m}{k}} v_{0}$

answer is B.

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Detailed Solution

Maximum expansion in spring is given by
$\frac{1}{2} {kx}_{max}^{2} = \frac{1}{2} {μv}_{0}^{2} [μ = Reduced mass] \Rightarrow x_{max} = \sqrt{\frac{μ}{k}} \cdot v_{0} = \sqrt{\frac{2 m}{3 k}} v_{0}$

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