Question

The string of a pendulum is horizontal initially. The mass of the bob attached is m. Now the string is released. 'R' is the length of the pendulum.
(i) The tension in the string at an angle ${30}^{\circ }$ with the vertical is ______

• A. $2\sqrt{9}mg$
• B. $2\sqrt{3}mg$
• C. $\frac{3\sqrt{3}}{2}mg$
• D. $4\sqrt{3}mg$

Answer 1

The correct option is D $4\sqrt{3}mg$

The string of a pendulum is horizontal initially. The mass of the bob attached is $m$. $R$ is the length of the pendulum,

(i) The tension in the string at an angle ${30}^o$, with the vertical is-

Conserving energy, velocity at lowest point is $(2gL{)}^{1/2}$.

Centripetal force= $\frac{m{v}^2}{R}=2mg$

$T-mg=\frac{m{v}^2}{R}$

$\Rightarrow \sin {30}^o=\frac{1}{2}$

$\Rightarrow \frac{2mg}{1/2}=4mg$

$4\sqrt{3}mg$ vertical tension .