Question

A pendulum is taken 1 km inside the earth from mean sea level. Then the pendulum

• A. loses 13.5 s per day
• B. gains 13.5 s per day
• C. looses 7s per day
• D. gains 7s per day

Answer 1

Answer: (C)

looses 7s per day

$g=g_o(1-\frac{h}{R})$ where, $h$ is the distance form the foresaw, and $h<<R$

$T_1=2\pi \sqrt{\frac{l}{g_o}}$

$T_2=2\pi \sqrt{\frac{l}{g_o(1-\frac{1}{6400})}}$

$T_2-T_1=2\pi \sqrt{\frac{l}{g_o}}\left(\sqrt{\frac{6400}{6399}-1}\right)$

$2\pi \sqrt{\frac{l}{g_o}}=1s$

Therefore, in one day $\delta T$ is $6.75s$.

Therefore, the pendulum will loose $7$ sec per day.