Question

A simple pendulum is oscillating with an angular amplitude ${60}^{\circ }$. The ratio of tensions in the string when the bob reaches the mean position and the extreme position respectively is :

• A. $2:1$
• B. $3:1$
• C. $1:3$
• D. $4:1$

Answer 1

The correct option is D $4:1$

At A
$T_A=mgcos{60}^0$
$T_A=\frac{mg}{2}$

By Work Energy Theorem from A to B
$mgR(1-cos{60}^0)=\frac{1}{2}m{V}^2$
$mg\frac{R}{2}=\frac{1}{2}m{V}^2$
$V=\sqrt{Rg}$

At B
$T_B-mg=\frac{m{V}^2}{R}$
$T_B=mg+mg=2mg$
$\therefore \frac{T_B}{T_A}=\frac{2mg}{mg/2}=4$