Question

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 angular displacement of the pendulum of the string with respect to the downward vertical.

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

The correct option is D ${90}^o$

Tension at the mean position,

$mg+\frac{m{v}^2}{r}$=3mg

v=$\sqrt{2}gl$ ......(1)

and if the body displaces by angle q with the vertical

then v=$\sqrt{2}gl(1-cos\theta )$.......(2)

comparing (1) and (2)

$cos\theta$= $0\rho \theta$=${90}^0$