A simple pendulum oscillates in a vertical plane. When it passes through mean position, tension in s

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5.Work, Energy, Power and Collision

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A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is $3$ times the weight of the pendulum bob. What is the maximum displacement of the pendulum of the string with respect to the vertical ......... $^o$.

A

$30$

B

$45$

C

$60$

D

$90$

Solution

(d) Tension at mean position, $mg + \frac{{m{v^2}}}{r} = 3\,mg$

$v = \sqrt {2gl} $…$(i)$

and if the body displaces by angle $\theta$ with the vertical then $v = \sqrt {2gl(1 – \cos \theta )} $…$(ii)$

Comparing $(i)$ and $(ii)$, $\cos \theta = 0$

$⇒$ $\theta = 90^\circ $

Standard 11

Physics

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