Q. The angular amplitude of a simple pendulum is $\theta_{0}$. The maximum tension in its string will be
A) $mg(1 - \theta_{0})$
B) $mg(1 + \theta_{0})$
C) $mg(1 - \theta_{0}^{2})$
D) $mg(1 + \theta_{0}^{2})$
Explanation
(d) Maximum tension in the string is
$T_{\max} = mg + \frac{mv_{B}^{2}}{l}$
[image:4_image85.emf]
$= mg + \frac{2mgl}{l}(1 - \cos\theta_{0})$
$= mg + \frac{2mgl}{l}.2\sin^{2}\frac{\theta_{0}}{2}$
$\because\left( 1 - \cos\theta_{0} = 2\sin^{2}\frac{\theta_{0}}{2} \right)$
[Since $\theta_{0}$ is small]
$= mg(1 + \theta_{0}^{2})$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.