Question

A simple pendulum with length L and mass m of the bob is vibrating with an amplitude a. Then, the maximum tension in the string is

• A. $ 2mk{{r}^{2}}t $
• B. $ mk{{r}^{2}}{{t}^{2}} $
• C. $ m{{k}^{2}}{{r}^{2}}t $
• D. $ m{{k}^{2}}r{{t}^{2}} $

Answer 1

Answer: (B)

Tension in the string $ T-mg\cos \theta =\frac{m{{v}^{2}}}{L} $ T is maximum, when $ \theta ={{0}^{o}} $
$ \therefore $ $ {{T}_{\max }}=mg+\frac{m{{v}^{2}}_{\max }}{L}=mg+\frac{m{{a}^{2}}{{\omega }^{2}}}{L} $ $ \because $ a is amplitude $ {{T}_{\max }}=mg+\frac{m{{a}^{2}}}{L}\times \frac{g}{L} $ $ =mg\left[ 1+{{\left( \frac{a}{L} \right)}^{2}} \right] $