Question

the value of of g becomes 1/4th of the value on earth at a depth h from the surface of earth what will be the value g at same height

Answer 1

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.