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

If radius of the earth is reduced by n times without changing its mass

1.	If radius of the earth is reduced by n times without changing its mass, then what will be the magnitude of g'_eat the surface of earth?
Answer» SOLUTION :`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`