Question

Acceleration due to gravity of a body during free fall does not depend upon the:
A) mass of earth
B) mass of body
C) universal gravitational constant
D) radius of earth

Answer 1

In this problem we are going to apply the concept of Newton’s second law and Newton's universal law of gravitation.According to Newton’s second law of motion,the rate of change of momentum of a body is directly proportional to the force applied on body.

Complete step by step answer:
Let us consider a body of mass m freely falling towards earth, M be the mass of the earth and R be the radius of earth.
As per Newton’s second law, the force exerted by the earth on the body is given by,
${F_1}=mg$ ----------(i)
Where F_1 is the force exerted on the body, m is the mass of the body and g is the acceleration due to gravity.
As per Newton’s universal law of gravitation, the force between the body and the earth is
${F_2}=\dfrac{GmM}{R^2}$ -----------(ii)
Where F_2 is the force between body and the earth, G is the gravitational constant, m is the mass of the body, M is the mass of the earth and R is the distance between earth and the body.
The magnitude of force exerted by earth on body and force exerted by body on the earth is equal and opposite in direction. By equation (i) and (ii) we get
${F_1}={F_2} \\\ \Rightarrow mg=\dfrac{GmM}{R^2}$ (m can be cancelled on both side)
Now, this equation can be reduced to
$\therefore g=\dfrac{GM}{R^2}$
Hence, we conclude that the acceleration due to gravity g is directly proportional to mass of the earth ‘M’ and inversely proportional to the square of the distance between them. Hence it is independent of the mass of the body.

The correct answer is option(B).

Note: In this question sometimes, we may get confused that g depends on the mass of the body. Here we must note down that anybody cannot apply force on itself and accelerate. Only it can apply force on another body and accelerate it.