Q. 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 with respect to the vertical
A) $30{^\circ}$
B) $45{^\circ}$
C) $60{^\circ}$
D) $90{^\circ}$
Explanation
(d) Tension at mean position, $mg + \frac{mv^{2}}{l} = 3mg$
$v = \sqrt{2gl}$
And if the body displaces by angle $\theta$ with the vertical
Then $v = \sqrt{2gl(1 - \cos\theta)}$
Comparing (i) and (ii), $\cos{\theta = 0 \Rightarrow \theta = 90{^\circ}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.