At what height from the surface of Earth the gravitational force will be reduced by 10% if the radius of Earth is 6400 km?

At what height from the surface of Earth the gravitational force will

1.	At what height from the surface of Earth the gravitational force will be reduced by 10% if the radius of Earth is 6400 km?
Answer» SOLUTION :Gravitational FORCE on the Earth surface `F_(s)=(GMm)/(R_(E)^(2))` Gravitational force at HEIGHT h `F_(h)=(GMm)/((R_(E)+h)^(2))` `THEREFORE(F_s)/(F_h)=((R_(E)+h)^(2))/(R_(E)^(2))=(10)/(9)` `3(R_(E)+h)=3.162R_(E)` `3h=(3.162-3)R_(E)` `=0.162R_(E)` `(R_(E)+h)/(R_E)=(3.162)/(3)` `therefore` Height h `=(0.162xx6400)/(3)` (or) h = 345.6 KM