Question

Fill up the blank with suitable
Acceleration due to gravity independent of ________

Answer 1

- Hint – Here we will proceed by using the concept of Newton’s second law of motion that is $F = m \times a$ (force $ = $ mass $ \times $acceleration). Acceleration $ = \dfrac{{Force}}{{Mass}}$.

Complete step-by-step solution -

Acceleration due to gravity is independent of mass. These two quantities are independent of each other. Light objects accelerate more slowly than heavy objects when forces other than gravity are also at work. In this case the object is falling but is not considered as a free fall.
A body of mass m falling under the influence of gravity has a force given as –
$F = \dfrac{{GMm}}{{{R^2}}}$
Here, G is gravitational constant
M- mass of 1st body
m-mass of 2nd body
R- distance between two bodies.
Here, M is the mass of Earth and R is the radius of Earth.
Also this force is the weight of the body which is given as
$F = mg$ $ \to $ weight
Thus, we get
$\dfrac{{GMm}}{{{R^2}}} = mg$
$g = \dfrac{{GM}}{{{R^2}}}$
All these are constants and do not change.
So we can say that
Value of g remains constant. G is a universal constant.
It does not depend upon the mass of the body falling.

Note – Whenever we come up with this type of question, one must know that acceleration due to gravity does not depend upon the mass of the object. Then we write the formula of force and calculate the acceleration due to gravity. (Here by using the formula we calculate acceleration due to gravity is independent of mass).