Question

Two particles are placed at some distance and the magnitude of gravitational force between them is F. If the mass of each of the two particles is doubled, keeping the distance between them unchanged, the new value of gravitational force, in terms of F, between them will be:

• A. $\frac{F}{4}$
• B. $4F$
• C. $\frac{F}{2}$
• D. $F$

Answer 1

Answer: (B)

$4F$

The force of gravitational attraction between the two bodies of mass ($M$) and ($m$) is $F=G\frac{Mm}{r^2}$.
Now, If masses of both objects are halved without changing distance between them or $M=2M$ and $2m$
Now, $F=G\frac{2M\times 2m}{r^2}=4G\frac{Mm}{r^2}$.
Thus, force becomes four times as we increase the masses to double without altering the distances.