Question

Let $\theta$ denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of the bob is m, then tension in the string is mg $\cos \theta$

• A. always
• B. never
• C. at the extreme position
• D. at the mean position

Answer 1

The correct option is C at the extreme position

For simple pendulum
$\frac{m{v}^2}{r}=T-mg\cos \varphi$
But when $\varphi =\theta$, i.e., the bob is at extreme position. its velocity is zero, hence the equation becomes: $T-mg\cos \theta =0$
$\Rightarrow T=mg\cos \theta$