Question

Two particles are placed at some distance. If the mass of each of the two particles is doubled, keeping the distance between them unchanged, the value of gravitational force between them will be

• A. 14 times
• B. 2 times
• C. 4 times
• D. Unchanged

Answer 1

The correct option is C

4 times

Numerical guidelines to solve the problem

1. The gravitational force between the two particles is determined at the initial condition using the gravity force equation.
2. When the masses of the particles are doubled, the gravitational force also increases. Similarly, the gravitational force is determined in this condition.
3. Finally, the ratio of the gravitational forces is calculated.

Step 1: Gravitational force between two particles

Gravitational force is the attraction force between two particles due to the presence of mass.

The gravitational force can be expressed as follows:

$F_1=\frac{G{m}_1{m}_2}{R^2}$

Here,

$F_1$ is the gravitational force.

$m_1$ and $m_2$ are the masses of the two particles respectively.

$R$ is the distance between the particles.

Step 2: Gravitational force between two particles when their masses are doubled

When the masses are doubled, the expression of the gravitational force can be expressed as follows:

$F_2=\frac{G\left(2m_1\right)\left(2m_2\right)}{R^2}$

Here, $F_2$ is the gravitational force between the two objects when the masses are doubled.

Step 3: Calculation of the ratio between the gravitational forces

$$\begin{gathered} \frac{F_2}{F_1}=\frac{{\displaystyle \frac{G\left(2m_1\right)\left(2m_2\right)}{R^2}}}{\frac{G\left(m_1\right)\left(m_2\right)}{R^2}} \\ \frac{F_2}{F_1}=4 \end{gathered}$$

Hence, when the masses of the particles are doubled, the gravitational force becomes $4$ times.