Correct Answer - Option 2 : 6 m/s
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The correct answer is option 2) i.e. 6 m/s2
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:
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.
- Therefore, the acceleration of the 6 kg mass at the same place is 6 m/s2 itself.