Question

What will be the time period of a simple pendulum length of string L >> R${}_2$ (Radius of earth)

Answer 1

time period for very large.

Length of string

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

Since $L>>R$

then $\frac{1}{L}<<\frac{1}{R}$

$\therefore \frac{1}{L}$ can be neglected in compare to $\frac{1}{R}$

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

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