Question

Angle of simple pendulum is ${60}^0$. Find the tension in string when string makes an angle of ${30}^0$ with the vertical:

• A. $mg\frac{\sqrt{3}}{2}$
• B. $(3\sqrt{3}-2)mg$
• C. $mg(\frac{3\sqrt{3}}{2}-1)$
• D. None of these

Answer 1

The correct option is C $mg(\frac{3\sqrt{3}}{2}-1)$

For simple pendulum,

$\therefore T=\frac{m{v}^2}{r}+mg\cos \theta ...\left(i\right)$

$\frac{1}{2}m{v}^2=(r\cos 30°-r\sin 30°)mg$...(energy conservation)

$\frac{m{v}^2}{r}=2[\frac{\sqrt{3}}{2}-\frac{1}{2}]mg=(\sqrt{3}-1)mg$

$\therefore$ Substituting $\frac{m{v}^2}{r}$ in equation $\left(i\right)$

We get,

$T=(\sqrt{3}-1)mg+mg\left(\frac{\sqrt{3}}{2}\right)$

$\because T=mg(\frac{3\sqrt{3}}{2}-1)$ Thus option C