A simple pendulum oscillates in a vertical plane. When it passes … - Vidyadip

MCQ

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
$60$
✓
$90$

✓

Answer

Correct option: D.

$90$

d
(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 $

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