If radius of the earth is reduced by n times without changing its mass, then what will be the magnitude of `g'_e` at the surface of earth?

Explanation

`implies g_(e) = n^(2) g_(e)` because
on the surface `g_e =(GM_e)/(R_e^2)`
After shrinks radius `R._(e) =R_(e)/n`
After shrinks `g_(e) =(GM_e)/R_e^2`
`:. g_e/(g._e) = (g._e)^2/(R_E^2)` but `R_e/n`
` = R_e^2/n^2 xx1/R_e`
`g_e/(g._e)=1/n^2`
`:. g_e=n^2 .g_e`