Question

A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is $3$ times the weight of the pendulum bob. what is the maximum displacement of the pendulum of the string with respect to the vertical ?

• A. $30^{\circ }$
• B. $45^{\circ }$
• C. $60^{\circ }$
• D. $90^{\circ }$

Answer 1

Answer: (D)

In mean position,

$T=3mg$
Net force, $T-mg=\frac{m{v}^2}{l}$
$3mg-mg=\frac{m{v}^2}{l}$
$\Rightarrow v=\sqrt{2gl}$
Let maximum displacement with respect to vertical is $\theta$, then
$\frac{1}{2}m{g}^2=mgh=mg(l-l\cos \theta )$
$\frac{1}{2}m(2gl)=mgl(1-\cos \theta )$
$\cos \theta =0\Rightarrow \theta =90^{\circ }$