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Relation between Linear and Angular Speed

A body is han...

Question

A body 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 $v = \sqrt{2 g l}$ , the tension in the string increases just after the striking by :

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3 mg

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2 mg

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none of these

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Solution

The correct option is D 2 mg
$L e t v e l o c i t y a f t e r t h e c o l l i s i o n b e V m v = 2 m V V = \frac{v}{2} = \frac{\sqrt{2 g l}}{2} i n i t i a l l y t h e T e n s i o n i s T_{1} = m g a f t e r c o l l i s i o n T_{2} - 2 m g = 2 m \frac{V^{2}}{l} = 2 m \frac{2 g l}{4 l} = m g \Rightarrow T_{2} = 3 m g T h u s, T_{2} - T_{1} = 2 m g$

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