Question

The gravitational force between two objects is F. If the masses of both objects are doubled and the distance between them is also doubled, then the gravitational force would become

• A. F/4
• B. 4F
• C. F
• D. 16F

Answer 1

The correct option is C

F

Given:

The gravitational force between two bodies is F.

Required to find:

The gravitational force between the bodies if their masses are doubled, and the distance between them is also doubled.

Solution:

1. From given, the gravitational force between two bodies $g=\frac{G{m}_1{m}_2}{r^2}=F$.
2. Now, as the masses of the bodies are doubled, and also the distance between them is doubled, the final masses will be 2m₁ and 2m₂. The distance between them would become 2r.
3. Let the final value of gravitational force $g\text{'}=\frac{G\left(2m_1\right)\left(2m_2\right)}{{\left(2r\right)}^2}=\frac{4G{m}_1{m}_2}{4r^2}=\frac{G{m}_1{m}_2}{r^2}=F$.

Hence, if the masses of the two objects are doubled, and the distance between them is also doubled, the value of the gravitational force (F) remains the same.

So, (C) F is the correct answer.