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Question
the weight of an object reduces by a factor of 4 as it is taken from the earth's surface to a height of 6400 km, determine the radius of earth .
the weight of an object reduces by a factor of 4 as it is taken from the earth's surface to a height of 6400 km, determine the radius of earth .
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Solution
Let R be the radius of the earth. Height to which the object of mass say ‘m’ is taken is, h = 6400000 m
The force of gravity on the object at that height is, F = GMm/(R+h)2
The weight of the object at the surface of the earth is, W = GMm/R2
Given, W = 4F
=> GMm/R2 = 4GMm/(R+h)2
=> 1/R2 = 4/(R+h)2
=> 1/R = 2/(R+h)
=> R + h = 2R
=> R = h = 6400000 m = 6400 km
Let R be the radius of the earth. Height to which the object of mass say ‘m’ is taken is, h = 6400000 m
The force of gravity on the object at that height is, F = GMm/(R+h)2
The weight of the object at the surface of the earth is, W = GMm/R2
Given, W = 4F
=> GMm/R2 = 4GMm/(R+h)2
=> 1/R2 = 4/(R+h)2
=> 1/R = 2/(R+h)
=> R + h = 2R
=> R = h = 6400000 m = 6400 km
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