Suppose the force of gravitation between two equal masses is F. If each mass is doubled keeping the distance of separation between them unchanged, the force would become
F
2 F
4 F
<img src="https://latex.codecogs.com/svg.latex? rac{1}{4}F" title=" rac{1}{4}F" />
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC NDA-1 – 2016
F = G * (m₁ * m₂) / r²
where G is the gravitational constant.
Initially, we have two equal masses, let’s call them m. So, m₁ = m and m₂ = m. The force is F = G * (m * m) / r² = G * m² / r².
Now, each mass is doubled, so the new masses are m₁’ = 2m and m₂’ = 2m. The distance of separation (r) remains unchanged.
The new force (F’) is:
F’ = G * (m₁’ * m₂’) / r²
F’ = G * (2m * 2m) / r²
F’ = G * (4 * m²) / r²
We can rewrite this as:
F’ = 4 * (G * m² / r²)
Since F = G * m² / r², we have F’ = 4 * F.
The force becomes four times the original force.