Question

A simple pendulum of length L swings in a vertical plane. The tension of the string when it makes an angle $\theta$ with the vertical and the bob of mass m moves with a speed v is (g is the gravitational acceleration):

• A. $m{v}^2/L$
• B. $mgcos\theta +m{v}^2/L$
• C. $mgcos\theta -m{v}^2/L$
• D. $mgcos\theta$

Answer 1

The correct option is B $mgcos\theta +m{v}^2/L$

Tension not only provides the centripetal force necessary for circular motion but also balances the component of weight along the string.

component of weight along the string is $mg\cos \theta$.

Thus, $T-mg\cos \theta =\frac{m{v}^2}{L}\Rightarrow T=mg\cos \theta +\frac{m{v}^2}{L}$.