Question

The bob of a simple pendulum is released when its string makes an angle $\theta$ with vertical. If the tension in the string is equal to thrice the weight of bob when the bob is at lowest point, the value of $\theta$ is:

• A. $30°$
• B. $45°$
• C. $60°$
• D. $90°$

Answer 1

The correct option is D $90°$

Apply WET between A and B,

$mgL(1-cos\theta )=\frac{1}{2}m{v}^2$
$v=\sqrt{2gL(1-cos\theta )}$
At pt. A,
$T-mg=\frac{m{v}^2}{L}$
Also, $T=3mg$
$3mg-mg=\frac{m{v}^2}{L}$
$\sqrt{2gL}=v=\sqrt{2gL(1-cos\theta )}$
$1=1-cos\theta$
$cos\theta =0$
$\theta ={90}^0$