Question

The maximum tension in the string of an oscillating pendulum is twice the minimum tension. What is its angular amplitude?

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${\sin }^{-1}\left(2/3\right)$
• D. ${\cos }^{-1}\left(3/4\right)$

Answer 1

The correct option is D ${\cos }^{-1}\left(3/4\right)$

The maximum and minimum tensions in the simple pendulum are given by
$T_{max}=3mg-2mgcos\theta$...(1) (At bottom of the swing)
$T_{min}=mgcos\theta$...(2) (At the maximum swing)
Given that $T_{max}=2T_{min}$, we can say that
$3mg-2mgcos\theta =2mgcos\theta$
Solving, we get $\theta =co{s}^{-1}\left(3/4\right)$
Hence, option d is correct.