A simple pendulum is taken at a place where its separation from the earth's surface is equal t the radius of the earth. Calculate the time period of small oscillations if the length of the string is 1.0m. Take `g=pi^2ms^-2` at the surface of the earth.

Explanation

Acceleration due to gravity at height `h=R_e`, `R_e`: radius of earth
`g^'=(g)/((1+h//R_e)^2)=(g)/((1+R_e//R_e)^2)=g/4`
`T=2pisqrt((L)/(g^'))=2xsqrt((1)/(g//4))=2pisqrt(4/g)`
`=2pisqrt((4)/(pi^2))=4s`