A body of mass m hangs at one end of a string of length l, other end of which is fixed. It is given

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5.Work, Energy, Power and Collision

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A body of mass $m$ hangs at one end of a string of length l, the other end of which is fixed. It is given a horizontal velocity so that the string would just reach where it makes an angle of ${60^°}$ with the vertical. The tension in the string at mean position is

A

$2\,mg$

B

$mg$

C

$3\,mg$

D

$\sqrt 3\, mg$

Solution

(a) When body is released from the position p (inclined at angle $\theta$ from vertical) then velocity at mean position

$v = \sqrt {2gl(1 – \cos \theta )} $

Tension at the lowest point = $mg + \frac{{m{v^2}}}{l}$

$ = mg + \frac{m}{l}[2gl(1 – \cos 60)]$$ = mg + mg = 2\,mg$

Standard 11

Physics

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