The depth at which the value of g becomes 25% of that at the surface of the earth
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Explanation :
g=GM/Re² =>at any depth h below the earth g becomes g'=GM'/(Re-h)².
Here M’=M[(4/3)π(Re-h)³/{(4/3)πRe³]
=M×{(Re-h)/Re}³.
So g’/g=[GM{(Re-h)³/Re³}/(Re-h)²]/[GM/Re²]
={(Re-h)/Re}.So g'/g={1-(h/Re)}
As the question indicates g'/g=0.25
=>[1-(h/Re)]=1/4
=>h/Re=1-(1/4)=3/4
=>h=(3/4)Re=(3/4)×6400=4800km.
ANS. 4800 km.
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