Question:
A body weighs 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth ?
Answer:
Weight of the body, W = 63 N
Acceleration due to gravity at height h from the Earths surface is given by the relation:
g prime = g / [1 + ( h / Re) ]2
Where,
g = Acceleration due to gravity on the Earths surface
Re = Radius of the Earth
For h = Re / 2
g prime = g / [(1 + (Re / 2Re) ]2
= g / [1 + (1/2) ]2 = (4/9)g
Weight of a body of mass m at height h is given as:
W prime = mg
= m × (4/9)g = (4/9)mg
= (4/9)W
= (4/9) × 63 = 28 N.
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