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,

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