First slide

Vertical circular motion

Question

A simple pendulum oscillates in a vertical plane. When it passes through the bottommost point, 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?

Moderate

A

30⁰
B

45⁰
C

60⁰
D

90⁰

Solution

At mean position, $m g + \frac{m v^{2}}{r} = 3 m g \Rightarrow v = \sqrt{2 g l}$ …(i)
and if the body displace by angle $θ$ with the vertical, then
$v = \sqrt{2 g l (1 - \cos θ)}$ …(ii)
On comparing Eqs. (i) and (ii), we get
$\cos θ = 0 \Rightarrow θ = 90 °$

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