A planet has a mass M₁ and radius R₁. The value of acceleration due to gravity on its surface is g₁. There is another planet 2, whose mass and radius both are two times that of the first planet. Which one of the following is the acceleration due to gravity on the surface of planet 2?
g₁
2g₁
g₁/2
g₁/4
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-2 – 2018
For planet 2, the mass M₂ = 2M₁ and the radius R₂ = 2R₁.
We can calculate the acceleration due to gravity on planet 2’s surface (g₂) using the same formula:
g₂ = G * M₂ / R₂²
Substitute the values for M₂ and R₂ in terms of M₁ and R₁:
g₂ = G * (2M₁) / (2R₁)²
g₂ = G * (2M₁) / (4R₁²)
g₂ = (2/4) * (GM₁/R₁²)
g₂ = (1/2) * (GM₁/R₁²)
Since g₁ = GM₁/R₁², we have g₂ = g₁/2.