Question

When the distance between two bodies of masses $m_1$ and $m_2$ is doubled, then the gravitational force between them is _________ of the initial gravitational force.

• A. $\frac{1}{4}th$
• B. $\frac{1}{5}th$
• C. 4 times
• D. twice

Answer 1

The correct option is A

$\frac{1}{4}th$

Step 1. Given data:

Masses are $m_1$and $m_2$

Distance between the masses is doubled

Step 2. Finding the change in the force:

Let the initial distance between the masses be d.

Then Gravitational force is given as,

$F_1=G\frac{m_1{m}_2}{d^2}$ ------------(1)

Now distance has become 2d.

Then the gravitational force is given as,

$F_2=G\frac{m_1{m}_2}{4d^2}$ -----------(2)

From equation (1) and (2) we can conclude that,

$F_2=\frac{1}{4}{F}_1$

Therefore the gravitational force between the masses has become one-fourth.

Hence the correct option is option (A).