The acceleration due to gravity on the earth's surface at the poles is g and angular velocity of the earth about the axis passing through the pole is ω . An object is weighed at the equator and a

Question

The acceleration due to gravity on the earth's surface at the poles is g and angular velocity of the earth about the axis passing through the pole is ω . An object is weighed at the equator and at a height h above the poles by using a spring balance. If the weights are found to be same, then h is: ( h ≪ R , where R is the radius of the earth)

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Acceleration due to gravity at height h above the pole is given by g h = g 1 - 2 h R . . . ( 1 ) Acceleration due to gravity at the equator due to rotation of the earth is given by g ' = g − ω 2 R cos 2 λ . . . ( 2 ) At the equator, λ = 0 ⇒ g ' = g − ω 2 R . . . ( 3 ) As both weights are equal, i.e.; g h = g ' From equation ( 1 ) and ( 2 ) , we get, ⇒ ω 2 R = 2 g R h ∴ h = R 2 ω 2 2 g

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