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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)

1. R²ω² / 8g
2. R²ω² / 4g
3. R²ω² / g
4. R²ω² / 2g

Correct answer: R²ω² / 2g

Solution

At the equator effective gravity is g - omega^2*R; at height h above a pole it is g(1 - 2h/R). Setting weights equal: g - omega^2*R = g - 2gh/R, so h = R^2*omega^2/(2g).

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