Question

The time period of a simple pendulum of infinite length is ($R=$ radius of earth).

• A. $\text{infinite}$
• B. $2\pi \sqrt{\frac{R}{g}}$
• C. $2\pi \sqrt{\frac{g}{R}}$
• D. $2\pi \sqrt{\frac{2R}{g}}$

Answer 1

The correct option is B $2\pi \sqrt{\frac{R}{g}}$

If the length of simple pendulum $\left(l\right)$ is comparable to radius of earth $\left(R\right)$, then time period

$T=2\pi \sqrt{\frac{1}{g(\frac{1}{l}+\frac{1}{R})}}$

If length become infinite,

$T=2\pi \sqrt{\frac{1}{g(\frac{1}{\infty }+\frac{1}{R})}}$

$\Rightarrow T=2\pi \sqrt{\frac{R}{g}}$

Hence, $\left(B\right)$ is the correct answer.