Question

The gravitational force between two objects is F. If masses of both the objects are halved without altering the distance between them, then the gravitational force would become:

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

Answer 1

The correct option is A $\frac{F}{4}$

Given, the gravitational force between the objects $=F$
Here, $F=\frac{GMm}{r^2}$
where $M=massofobject1$
$m=massofobject2$
$r=distancebetweentheobjects$
Masses of both the objects are halved, hence the new gravitational force F’ becomes:
$F^{\prime }=G\times \frac{\left[\right(\frac{M}{2})\times (\frac{m}{2}\left)\right]}{\left(r2\right)}$
$F^{\prime }=\frac{\left(GMm\right)}{\left(4r^2\right)}$
$\Rightarrow F^{\prime }=\frac{1}{4}\times \frac{GMm}{r^2}$
$\Rightarrow F^{\prime }=\frac{F}{4}$