Question

Does acceleration due to gravity depend upon the mass of the body ?

Answer 1

No, acceleration due to gravity do not depend on the mass of the body.

The acceleration produced in a freely falling body by the gravitational pull of the earth is called the acceleration due to gravitation.

We know that,

Force = Mass $\times$ Acceleration

$F=m\times a$

$a=\frac{F}{m}$ ...........1

Where $F$ is the force on the object of mass $m$ dropped from a distance r from the centre of earth of mass $M$.

So, force exerted by the earth on the object is

$F=G\frac{M\times m}{r^2}$ ..........2

$M$ = Mass of Earth

$m$ = mass of object

$r$ = distance of object from centre of earth

Now, from equation 1 and 2,

$a=G\frac{M\times m}{r^2\times m}$

$a=G\frac{M}{r^2}$

Now, from above,

$a=g$ = Acceleration due to gravity

We also see that, although force is depending on the mass of the object,

$F=G\frac{M\times m}{r^2}$

But acceleration due to gravity is independent of the mass.

$g=G\frac{M}{r^2}$