Question

The time period of a simple pendulum of infinite length is $(R_e=$ radius of Earth)

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

Answer 1

Answer: (A)

For an infinite length pendulum, the arc would be a straight-line. The restoring force is $mg\cos \theta$ as shown, but $\cos \theta$
$=\frac{x}{R_e}$
$\Rightarrow F=-mg\cos \theta =-\frac{mgx}{R_e}$
$F=-\left(\frac{mg}{R_e}\right)x$
$\Rightarrow T=2\pi \sqrt{\frac{m}{k}}$
$\Rightarrow T=2\pi \sqrt{\frac{R_e}{g}}$