Figure shows a ball of mass m connected with two ideal springs of force constant K, kept in equilibrium on a smooth incline, suddenly right spring is cut. What is the magnitude of instantaneous acceleration $(in \frac{m}{s^{2}})$ of ball ? (Take ${g =10 ms}^{-2}$ )

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answer is 5.

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Detailed Solution

Initially $m g \sin 45^{o} = 2 k x \cos 45^{o}$

$\Rightarrow k x = \frac{m g}{2} ... (i)$

$Σ F_{x} = m a_{x} \Rightarrow m g \sin 45^{o} - k x \cos 45^{o} = m a_{x}$

$a_{x} = \frac{g}{2 \sqrt{2}} Σ F_{y} = m a_{y} \Rightarrow a = \frac{g}{2 \sqrt{2}} (\hat{i} + \hat{j})$

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