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 increas
• 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

Answer 1

Answer: (D)

The acceleration due to gravity at point $P$ having latitude $\lambda$ is given by

$g^{\prime }=g-R{\omega }^2{\cos }^2\lambda$
$\Rightarrow M{g}^{\prime }=mg-mR{\omega }^2{\cos }^2\lambda$
At equator: $\lambda =0^{\circ };m{g}^{\prime }=mg-mR{\omega }^2$
At pole: $\lambda =90^{\circ };m{g}^{\prime }=mg-mR{\omega }^2{\cos }^{2}90^{\circ }$
$\Rightarrow m{g}^{\prime }=mg$
That is, weight of the object at poles remains unchanged. Thus, the difference in weight is
$\left(mg-m{g}^{\prime }\right)=mR{\omega }^2{\cos }^2\lambda$
Therefore, the loss in weight depends upon latitude $\lambda$. The effect is maximum at equator.