Q. Let is the angular velocity of the earth's rotation about its own axis and acceleration due to gravity on the earth's surface at the poles is . An object weighed by a spring balance gives the same reading at the equator, as well as at a height above the poles ( ). What is the value of ?

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Solution:

The value of acceleration due to gravity at the equator is and the acceleration due to gravity at a height h above the pole is . It is given that