Question

The string of a pendulum of length $l$ is displaced through ${90}^{\circ }$ from the vertical and released. Then the minimum strength of the string in order to withstand the tension as the pendulum passes through the mean position is:

• A. $2mg$
• B. $6mg$
• C. $3mg$
• D. $5mg$

Answer 1

The correct option is C $3mg$

Let the velocity of the pendulum at the mean position i.e $O$ be $v$ and tension be $T$

Using work-energy theorem from A to O : $W_g=\Delta K.E$

$mgl=\frac{1}{2}m{v}^2$ $⟹m{v}^2=2mgl$ .......(1)

Circular motion equation at point O : $\frac{m{v}^2}{l}=T-mg$

From (1) we get $\frac{2mgl}{l}=T-mg$

$\therefore$ $2mg=T-mg$ $⟹T=3mg$