Question

If the length of a simple pendulum is equal to the radius of the earth, its time period will be

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

Answer 1

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

We know, for a pendulum of large length $L$, the time period is given by

$T=\sqrt{\frac{R_e}{(1+R_e/L)g}}$

Where $R_e$ is the radius of the earth

when $L=R_e$

Then $T=2\pi \sqrt{\frac{R_e}{(1+R_e/R_e)g}}$

$T=2\pi \sqrt{\frac{R_e}{2g}}$
Hence the correct answer is $\left(B\right)$