Question

A simple pendulum with length $l$ and mass $m$ of the bob is vibrating with amplitude $a$. The the maximum tension in the string is

• A. $mg{[1+\frac{a}{l}]}^2$
• B. $mg[1+{\left(\frac{a}{l}\right)}^2]$
• C. $mg$
• D. $mg{[1+\frac{a}{2l}]}^2$

Answer 1

Answer: (B)

$mg[1+{\left(\frac{a}{l}\right)}^2]$

The tension in the string would be maximum when bob will be passing through the mean position

$T_{max}=mg+\frac{m{v}^2}{l}$

At mean position, $v=a\omega$ and $\omega =\sqrt{\frac{g}{l}}$

$T_{max}=mg+\frac{m{\left(a\omega \right)}^2}{l}$

$=mg+\frac{m}{l}\left(\frac{a^{2}g}{l}\right)$

$=mg(1+\frac{a^2}{l^2})$