a certain height above the earth’s surface, the acceleration due to gravity is 10% of its value at the earth surface. Determine the height.[ R=6400km]
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Acceleration due to gravity at a height, h=4% of g.
Radius of earth, R=6400 K.M=6.4×106 m.
∴gh=4100g But gh=g⋅R2(1+hR)2
∴4100g=g1+hR2⇒(1+hR)2=1004
Take roots on both sides then, 1+hR=102
=5⇒1+hR=5⇒hR=5−1=4
∴h=4R=6400×4=25,600 k.m.
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