Given weight,

\(1.5=\frac{\frac{ GM }{ R ^2}-\frac{ GM }{( R + h )^2}}{\frac{ GM }{ R ^2}}\)

\(=\frac{ R ^2+2 Rh + h ^2- R ^2}{( R + h )^2}\)

\(\Rightarrow \frac{2 Rh + h ^2}{( R + h )^2}=\frac{1.5}{100}\)

At depth ' \(h, g\) ' \(=g\left(1-\frac{h}{R}\right)\)

SO g' decreases, \(\frac{g-g}{g}=\frac{h}{R}\)

\(\Rightarrow \frac{\frac{2 h }{ R }+\left(\frac{ h }{ R }\right)^2}{\left(1+\frac{ h }{ R }\right)^2}=\frac{1.5}{100}\)

\(\frac{2 h }{ R }=\frac{1.5}{100}\)

\(\frac{ h }{ R }=\frac{0.75}{100}\)

But since \(h \ll \ll R\)

At depth ' \(h\) there will be a decrese of \(g\) by \(0.75 \%\)