Question

The value of acceleration due to gravity on the surface of the earth depends on
(A) Pressure
(B) Acceleration
(C) Gravitational force between an object and the earth
(D) None of these

Answer 1

Hint The weight of a body is the effect of gravitational attraction of the body to the earth. According to Newton’s law the force of attraction between two bodies is directly proportional to the product of their masses, and inversely proportional to the square of the distance of their centers.

Formula used: $ W = mg $ where $ W $ is the weight of the body with mass $ m $ and $ g $ is the acceleration due to gravity. $ {F_g} = \dfrac{{GmM}}{{{r^2}}} $ , where $ {F_g} $ is the gravitational force of attraction between mass $ m $ and $ M $ , while $ r $ is the distance between their centers.

Complete step by step answer
The weight of a body of mass is given by $ m $ is given by
 $\Rightarrow W = mg $ where $ g $ is the acceleration due to gravity.
Weight is an effect of the gravitational force between the earth and that of the body.
Hence,
 $\Rightarrow {F_g} = mg $
But fundamentally, $ {F_g} $ according to Newton’s universal law of gravitation, is given by
 $\Rightarrow {F_g} = \dfrac{{GmM}}{{{r^2}}} $ where $ m $ is the mass of the body and $ M $ is the mass of the earth, while $ r $ is the distance between their centers.
Then from $ {F_g} = mg $ , $ g $ can be written as
 $\Rightarrow g = \dfrac{{{F_g}}}{m} $
Hence $ g $ is dependent on $ {F_g} $ , therefore acceleration due to gravity on the surface of the earth depends on the gravitational force between the object and the earth.

Note
A common error is to reason that the gravitational force depends on acceleration due to gravity and not the other way around. This is due to the popular belief that the acceleration due to gravity is constant. Such students may go for option D. Fortunately, a simple way to reason correctly is to remember that forces always cause acceleration and not vice versa. Also, the acceleration due to gravity isn’t exactly constant. Since it depends on the gravitational force, which in turn depends on the distance of the body from the center of the earth, it changes with increase in height but is fairly constant for a few hundred to thousand meters above ground.