Question

what is the time period of simple pendulum at centre of earth

Answer 1

When we've a pendulum at the center of an earth, there are different cases that how we will position it. A pendulum has a limited size, so there are two alternatives which are:  

1. The bottom / base of the swinging arc of the pendulum is at the center of the Earth.  
2. The end of the rope of the pendulum is at the center of the Earth.  

A basic pendulum's period is essentially dependent on the speeding up because of gravity: the value g. The magnitude / size of this variable changes w .r. t. mass of a gravitational body, and has a course toward said body's focal point of mass. On the Earth's surface, its mass is focused below, giving the value g a genuinely uniform size and direction. Yet, as we move toward the Earth's inside, increasingly more of the planet's mass surrounds the pendulum with that the net estimation of g diminishes. At the inside, the planet's mass is pretty much equitably encompassing the pendulum with the end goal that the net estimation of g is zero and it is basically weightless. Without weight, there is no re-establishing power / restoring force to keep up S.H.M, and the periodicity no longer exists.