Correct Answer - Option 4 : All of the above
The correct answer is option 4) i.e. All of the above
CONCEPT:
-
Law of Universal Gravitation: It states that all objects attract each other with a force that is proportional to the masses of two objects and inversely proportional to the square of the distance that separates their centres.
It is given mathematically as follows:
\(F = \frac{Gm_1m_2}{R^2}\)
Where m1 and m2 are the mass of two objects, G is the gravitational constant and R is the distance between their centres.
- From the Law of Universal Gravitation, the gravitational force acting on an object of mass m placed on the surface of Earth is:
\(F = \frac{GMm}{R^2}\)
Where R is the radius of the earth.
From Newton's second law, F = ma = mg
\(⇒ mg =\frac{GMm}{R^2}\)
⇒ Acceleration due to gravity, \(g =\frac{GM}{R^2}\)
EXPLANATION:
- The force of gravity acting on an object is directed towards the centre of the Earth i.e. towards the surface. So, the acceleration due to gravity is always vertically downward.
We know that acceleration due to gravity, \(g =\frac{GM}{R^2}\). Clearly, g depends on the mass of the planet (M) and not on the mass of the object that experiences acceleration due to gravity. So, g is independent of mass.
- Also, \(g \propto \frac{1}{R^2}\). Hence, it is inversely proportional to the square of the distance between two objects.
