1. Tardigrade
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  4. A body is hanging from a rigid support by an inextensible string of length l. It is struck inelastically by an identical body o f mass m with horizontal velocity V=√2gl, the tension in the string increases just after striking by

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Q. A body is hanging from a rigid support by an inextensible string of length $l$. It is struck inelastically by an identical body o f mass $m$ with horizontal velocity $V=\sqrt{2gl}$, the tension in the string increases just after striking by

AFMCAFMC 2012

Solution:

$m v_{o}=(m +m) v$
$v =\frac{v_{o}}{2}$
$T =\frac{2 m v^{2}}{l}+2\, m g$
$T =\frac{2 m v_{0}^{2}}{4 l}+2 m g$
$=\frac{m(2 g l)}{2 l}+2\, m g$
$T =3\, m g$
Increase in tension $=3\, mg - mg =2\, mg$