At what depth below the surface of the earth will the acceleration due to gravity decreases by 1% with respect to that on the earth's surface ? The earth can be taken as a uniform sphere of radius 6400 km.

Explanation

If the acceleration due to gravity on the earth.s surface is g, then at a depth h below the earth.s surface,
`g^.=g(1-h/R)=g-(gh)/R`
`therefore` Decrease in value ,`g-g^.=(gh)/R`
As per the question ,
`(gh)/R=0.01g`
or, `h=0.01xxR=0.01xx6400 =64 km`.