Question

Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence :

• A. Weight of the object, everywhere on the earth, will increase.
• B. Weight of the object, everywhere on the earth, will decrease.
• C. There will be no change in weight anywhere on the earth.
• D. Except at poles, weight of the object on the earth will decrease.

Hint:

Effective gravity at latitude \(\lambda\) is \(g'=g-\omega^2R\cos^2\lambda\); at the poles \(\cos\lambda=0\).

Answer 1

The Correct Option is D

Apparent weight \(=mg'\) with \(g'=g-\omega^2R\cos^2\lambda\), where \(\lambda\) is the latitude.
If \(\omega\) increases, \(\omega^2R\cos^2\lambda\) increases for every latitude except \(\lambda=90^\circ\) (poles), where it is zero.
So weight decreases everywhere except at the poles, where it is unchanged.
Answer: (4) Except at poles, weight of the object on the earth will decrease.