Question

Assertion (A): The value of 'g' is greater at the poles than at the equator.
Reason (R): Radius is more at the equator than at the poles.​

Answer 1

Explanation:

assertion is correct and reason is correct explanation of assertion

Answer 2

The assertion and its respective reason given in the question is completely true.    

• The Newton's Law of Gravitation states that the force of gravitation between two independent bodies is directly proportional to the product of the masses of both the individual bodies and is inversely proportional to the square of the distance between the centers of two bodies given the two bodies are kept some distance apart.
• The law of gravitation is visible in the revolution of moon around the earth, earth around the sun , a ball kept on the surface of earth etc.
• The Gravitational force between Earth of mass $M$ and a stone of mass $m$ separated by a finite distance lets say $R$ is given by

                                           $F=G\frac{Mm}{R^{2} }$

   Where $G$ is the universal gravitational constant $G=6.67$ ×$10^{-11}Nm^{2} /kg^{2}$

• Newton's second law of motion states that the force applied on a body is directly proportional to the rate of change of momentum of the body.

        Mathematically,          $F=\frac{dP}{dt}$  

                                            $F=ma$

         where, $a$ is the acceleration of the body.

For the stationary stone kept on the surface of the earth, there is no motion produced by the stone, Hence, in such cases, the acceleration on the body is nothing else but the acceleration due to gravity or purely its weight.

$F=mg$  

Equating both the fores, we get

$G\frac{Mm}{R^{2} }=mg$                                            

$g=\frac{GM}{R^{2} }$

Therefore, we see that the acceleration due to gravity is inversely proportional to the distance between the centers of the two bodies.  

$g$ ∝ $\frac{1}{R^{2} }$  

We know, earth is dimensionally an elliptical shape. The important property of the ellipse is that the radius of the ellipse is longer at the latitude or equator and comparatively shorter at the poles or longitude.

Hence,

• At poles, the radius of the earth is lower. Therefore, the value of acceleration is in greater at the poles than at the equator.
• At the equator, the radius of earth taken from the center to the equatorial circumference of the earth is greater as compared to the radius at poles. Therefore, the acceleration due to gravity is greater at the equator than at the poles.

Hence, the assertion and its respective reason given in the question is completely true.