Question

Consider two point masses separated by a particular distance. Now, if the masses are tripled, and the distance of separation is also tripled, then what will happen to the gravitational force between them?

• A. It gets tripled.
• B. It increases by 9 times.
• C. It decreases by 9 times.
• D. It remains the same.

Answer 1

The correct option is D It remains the same.

Let $m_1$ and $m_2$ be the masses.
Let the distance of separation be $r$

Initial force $F=\frac{G{m}_1{m}_2}{r^2}$

Now when the masses and the distance of separation are tripled,

New masses will be $3m_1$ and $3m_2$
New distance of separation = $3r$

Force of gravitation $F^{\prime }=\frac{G\times 3m_1\times 3m_2}{{\left(3r\right)}^2}$
$\Rightarrow F^{\prime }=\frac{G\times 9m_1{m}_2}{9r^2}$
$\Rightarrow F^{\prime }=\frac{G{m}_1{m}_2}{r^2}$
$\Rightarrow F^{\prime }=F$

Hence, the force remains the same.