Question

The time period of a simple pendulum of infinite length is:

• A. $T=2\pi \sqrt{\frac{R_e}{g}}$
• B. Infinity
• C. $T=\pi \sqrt{\frac{R_e}{g}}$
• D. Zero

Answer 1

The correct option is A $T=2\pi \sqrt{\frac{R_e}{g}}$

If the length of the pendulum considerably large.

$T$ $=$ $2\pi \sqrt{\frac{1}{g(\frac{1}{l}+\frac{1}{R})}}$ where $R$ $=$ radius of earth, $l$ $=$ length of the pendulum

In case of pendulum of infinite length the time period $T$ $=$ $2\pi \sqrt{\frac{R}{g}}$ where R $=$ radius of earth, g $=$ acceleration due to gravity

As seen from above formula, the time period is $T=2\pi \sqrt{\frac{R_e}{g}}$ and hence option A is correct.