Question

The time period of a simple pendulum of infinite length is $\left(R_{e}=\right.$ radius of Earth)

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

Answer 1

Answer: (A)

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