A box is hanging from a rigid support by an inextensible string of length 'l ' . It is struck inelastically by an identical body of mass m with horizontal velocity $v = \sqrt{2 gl} .$ The tension in the string increases just after the striking by x mg. Then x is

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answer is 2.

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Detailed Solution

From LCLM: ${mv}_{0} = (m + m) v \Rightarrow v = \frac{v_{0}}{2}$
$T = \frac{(2 m) v^{2}}{l} + (2 m) g = \frac{m (2 gl)}{2 l} + 2 mg = 3 mg$
Initial tension $T_{0} = mg \Rightarrow ΔT = 2 mg$

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