Question

The gravitational force with which a body is attracted towards the earth is:
A. The same at all the places on the earth surface
B. Minimum at the equator and maximum at the poles
C. Maximum at the equator and minimum at the poles
D. Independent of the place on the earth’s surface

Answer 1

We know that gravitational force is the force by which a body is attracted towards the center of the earth. This gravitational force is dependent on the value of gravitational acceleration at a particular point which is related to the distance of that location from the center of the earth. Therefore, we need to consider the distance of the equator and poles from the center of the earth to solve this problem.

Formulas used:
$W = mg$, where, $W$ is weight of the body, $m$ is mass of the body and $g$ is acceleration due to gravity
F = \dfrac{{GMm}}{{{r^2}}} \Rightarrow F = \dfrac{{GMm}}{{{r^2}}} \\\ \Rightarrow {g_r} = \dfrac{{GMm}}{{{r^2}}} \\\
Where, $F$ is the gravitational force, $G$ is the gravitational constant, $M$ is mass of the earth, $m$ is mass of the body and $r$ is the distance of the body from the center of the earth

Complete step by step solution:
We know that weight of the body $W = mg$.
This weight is nothing but the gravitational force at that particular location which is,
$F = \dfrac{{GMm}}{{{r^2}}}$.
From both these equations, we can say that gravitational acceleration at distance $r$ from the center of the earth is given by,
${g_r} = \dfrac{{GMm}}{{{r^2}}}$
-This means that gravitational acceleration is inversely proportional to the square of the distance of the body from the center of the earth which implies that as the distance increases, the gravitational acceleration decreases. This decrease in gravitational acceleration caused reduction in weight.
-Now, we know that earth is not perfectly spherical. The distance of the equator from the center of the earth is greater than that of the poles. As a result, gravitational acceleration is lower at the equator as compared to the poles. Therefore, it is clear that the gravitational force is minimum at the equator and maximum at the poles.

Hence, option B is the right answer.

Note: Besides the distance from the center of the earth, there is one more parameter that affects the gravitational force at a particular location. This parameter is the centrifugal force which is caused by the rotation of the earth. This force acts away from the axis of the rotation and can reduce the gravitational force. At the equator, this centrifugal force acts maximum directly opposite to gravitational force causing minimum gravitational force. But at the poles, the centrifugal force is zero due to which the gravitational force is maximum.