Question

At what height from earth will the value of g be 64% of the value of g on earth's surface ? (Radius of earth is 6400 km)
Answer is (1600 km)

Answer 1

Force of gravitation on an object of mass m at an altitude h from Earth's surface distance  be F.  Radius of Earth = Re    and mass of Earth be Me.

$F = G \frac{M_e \ m}{(Re + h)^2}= mg'\\\\So\ g'=\frac{GM_e}{(R_e+h)^2}\\\\g=\frac{GM_e}{R_e^2}\\\\\frac{g'}{g}=(\frac{R_e}{R_e+h})^2=64/100\\\\So\ \frac{R_e}{R_e+h}=0.8\\\\h=\frac{R_e}{4}=1600\ km$