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A simple pendulum is taken at a place wh...

A simple pendulum is taken at a place where its separation from the earth's surface is equal to 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.

Text Solution

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At a height R (radis of the earth) the acceleration due to gravity ils
`g'=(GM)/((R+R)^2)=1/4 (GM)/R^2=g/4`
The time period of small oscillations of the simple pendulum is
`T=2pisqrt(l/g')=2pi (sqrt(1.0m)/(1/4xxpi^2ms^-2))=2pi(2/pis)=4s`
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