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A ball of mass m = 1 kg is hung from a spring of constant 400 N/m and another ball of mass 2m is hanging from it as shown with the help of a thread. The system is in equilibrium. Now the thread is burned. As result, ball of mass ‘m’ starts moving upwards. Eventually it will stop under the influence of gravity and spring. In between, there is a point at which its speed is maximum. What is that maximum speed (in m/s)?

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Detailed Solution

$3 m g = k x_{i}, m g = k x_{0}$

maximum speed is at equilibrium $= A ω = \frac{2 m g}{k} \times \sqrt{\frac{k}{m}} = 2 g \sqrt{\frac{m}{k}} = 20 \times \sqrt{\frac{1}{400}} = 1 m / s .$

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