Mass m = 10 kg shown in figure is in equilibrium. If it is displaced further by x = 1 cm and released find its acceleration (in cm / s 2 ) just after it is released. Take pulleys to be light & smooth

Question

Mass m = 10 kg shown in figure is in equilibrium. If it is displaced further by x = 1 cm and released find its acceleration (in cm / s 2 ) just after it is released. Take pulleys to be light & smooth and strings light. (Take k = 10 N / m ) m = 10 kg x = 1 cm ( k = 10 N / m ) ​

TestHub · Accepted Answer

In equilibrium, the spring force balances $m g$

An extra displacement $x$ stretches the spring by $2 x$ on each side through the pulley, giving extra force $2 k (2 x) = 4 k x$

$a = \frac{4 k x}{m} = \frac{4 \times 10 \times 1}{10} = 4$ cm/s $^{2}$

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