First slide

Vertical circular motion

Question

A body is hanging from a rigid support by an inextensible string of length I. 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 striking by {AFMC 2012]

Easy

A

mg
B

3 mg
C

2 mg
D

None of these

Solution

Tension in the string,
$T = \frac{2 m {(v^{'})}^{2}}{l} + 2 m g = \frac{m (2 g l)}{2 l} + 2 m g$
$(∵ \frac{2 m {(v^{'})}^{2}}{l} = Centrifugal force and v^{'} = \frac{v}{2} = \sqrt{\frac{g l}{2}})$
$∴$ Increase ill tension = $3 m g - m g = 2 m g$

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