Correct Answer - Option 1 : 3.3 m/s
2
The correct answer is option 1) i.e. 3.3 m/s2
CONCEPT:
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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 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 = \(\frac{GM}{R^2}\)
CALCULATION:
Let acceleration due to gravity on Earth, g = \(\frac{GM}{R^2}\)
Let acceleration due to gravity on the planet be g'.
Given that:
Mass of the planet = 3 × Mass of earth ⇒ M' = 3 × M
Diameter of the planet = 3 × Diameter of earth ⇒ D' = 3 × D ⇒ Radius of planet, R' = 3 × Radius of earth = 3 × R
g' = \(\frac{GM'}{R'^2} = \frac{G(3M)}{(3R)^2} \)
= \(\frac{1}{3}\frac{GM}{R^2}\) = \(\frac{1}{3}\) × 9.81 = 3.27 m/s2 ≈ 3.3 m/s2
