Gravitation Reasonings

At what point of the earth’s surface will a body weigh more?

The weight of a body depends upon the acceleration due to gravity i.e. $W=mg$. The value of acceleration due to gravity is different on different points of the earth’s surface. We have the following relation for acceleration due to gravity, \[g=\frac{GM}{R^2}\]

Earth is slightly bulged at the equator. So, the radius $R$ is more in the equator. Hence, the value of $g$ as well as the weight of the body will be less there. The radius is less at poles, so $g$ and weight of the body will be more at poles.

The rotation of earth about its axis also causes difference in the value of $g$. The acceleration due to gravity considering the rotation of the earth is, \[g’=g-\omega^2R\cos^2\theta\]

At poles, $\theta=90°$ so $g’=g$ which means it has high value. At the equator, $\theta=0°$ so $g’=g-\omega^2R$ which means it has less value.