Question

The bob of a simple pendulum of mass m is oscillating with angular amplitude ${40}^{\circ }$. The tension in the string at the instant when its angular displacement is ${20}^{\circ }$ will be:

• A. $mg\cos {20}^{\circ }$
• B. $>mg\cos {20}^{\circ }$
• C. $<mg\cos {20}^{\circ }$
• D. mg

Answer 1

The correct option is B $>mg\cos {20}^{\circ }$

Since Amplitude is $40$ degree and particle is at $20$ degree, there will be some velocity.
Now, $T-mgcos{20}^0=\frac{m{v}^2}{l}$
$T=mgcos{20}^0+\frac{m{v}^2}{l}$
hence, option B is correct.