Question

The value of g is:
A. Maximum at poles
B. Maximum at equator
C. Same everywhere
D. Minimum at poles

Answer 1

Hint: The value of g varies with the angle made by the lines joining the point on the surface of the earth to the center with the equator. The value increases as the angle becomes larger. This is due to the effect of the rotation of the earth.

Formula used:
The value of acceleration due to gravity $g$at a point on the earth’s surface is given by
$g={{g}_{0}}\left( 1-\dfrac{{{\omega }^{2}}R{{\cos }^{2}}\theta }{{{g}_{0}}} \right)$
where ${{g}_{0}}$ is the acceleration due to gravity at the poles, $\omega $ is the angular frequency of rotation of the earth and $R$ is the radius of the earth.
$\theta $ is the angle made by the lines joining the point on the surface of the earth to the center with the equator.

Complete step by step answer:
Due to the rotation of the earth, bodies on the surface of the earth require a certain centripetal force to keep rotating along with the earth. At different points on the surface, the magnitude of centripetal force required changes since the effective radius of rotation changes. A component of the gravitational force provides this centripetal force.
Now, since, the centripetal force changes, the component of the gravitational force also changes. This variation depends on the angle made by the lines joining the point on the surface of the earth to the center with the equator.
Hence, at different points on the earth’s surface, the acceleration due to gravity is different.
The value of acceleration due to gravity $g$ at a point on the earth’s surface is given by
$g={{g}_{0}}\left( 1-\dfrac{{{\omega }^{2}}R{{\cos }^{2}}\theta }{{{g}_{0}}} \right)$ --(1)
where ${{g}_{0}}$ is the acceleration due to gravity at the poles, $\omega $ is the angular frequency of rotation of the earth and $R$ is the radius of the earth.
$\theta $ is the angle made by the lines joining the point on the surface of the earth to the center with the equator.
At the equator, $\theta ={{0}^{0}},\cos \theta =1,{{\cos }^{2}}\theta =1$, therefore according to (1), $g$ will be least, whereas at the poles $\theta ={{90}^{0}},\cos \theta =0,{{\cos }^{2}}\theta =0$, therefore according to (1), $g$ will be maximum.
Therefore, the correct answer is A) maximum at poles.

Note: An easy analogy to remember this concept is to relate this with a bar or horseshoe magnet. The magnetic force is maximum felt at the ends of the bar magnet or horseshoe magnet. The ends are also called poles. Hence, it can be remembered that similar to a bar magnet, the gravitational force is also felt maximum at the poles of the earth, while similar to a bar magnet, the gravitational force is felt least at the middle, or the equator.