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At what height above the surface of the earth, the value of g becomes 64% of its value on the surface is the earth. Radius of earth = 6400 km.




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We just use the Newton's law of gravitation.  that is simple.
Let the Force of gravitation on an object of mass m at an altitude h from Earth's surface distance  be equal to F.

let  Radius of Earth = Re = 6400 km
      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

So the altitude = h=\frac{R_e}{4}=1600\ km

at a height of 1/4 th of Earth's radius..

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