The value of acceleration due to gravity at the depth of d below Earth’s surface,
g’ = \(g\left(1-\frac{d}{R}\right)\)
where g is the acceleration due to gravity at Earth’s surface and R is its radius.
For the centre of the earth,
d = R
∴ g’ = \(g\left(1-\frac{R}{R}\right)\) = g (1 - 1)
or g’ = 0
∴ The time period of simple pendulum.
T = \(2 \pi \sqrt{\frac{l}{g^{\prime}}}=2 \pi \sqrt{\frac{l}{0}}\) = ∞ (infinity)
Thus the time period of the watch based on simple pendulum will be infinite i.e., the watch will not work.
