Correct Answer - Option 4 : none of the above
The correct answer is option 4) i.e. none 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
\(⇒ mg =\frac{GMm}{R^2}\)
Therefore, acceleration due to gravity, \(g =\frac{GM}{R^2}\)
EXPLANATION:
We know that acceleration due to gravity, \(g =\frac{GM}{R^2}\)
- For the value of g to be infinity for a celestial body, either its mass (M) should be infinite or its radius (R) should be zero.
- These conditions cannot be followed in a real object.
- Therefore, such a celestial body is not possible on which the value of g is infinite.
- Hence, none of the given options is true.
