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The gravitational force between two objects is $F$. If masses of both objects are halved without changing distance between them, then the gravitational force would become
$(a).\ F/4$
$(b).\ F/2$
$(c).\ F$
$(d).\ 2F$
As known that the force of attraction between the two objects is inversely proportional to the square of the distance between the two objects.
So, $F=G\frac{m_1m_2}{r^2}$
Here, $F\rightarrow$ force of attraction between the two objects.
$r\rightarrow$ distance between the two objects.
$m_1$ & $m_2\rightarrow$ masses of the two objects
If the masses of both the two objects are halved, then they will become $\frac{m_1}{2}$ and $\frac{m_2}{2}$.
Then, force of attraction, $F'=G\frac{\frac{m_1}{2}\times \frac{m_2}{2}}{r^2}$
Or $F'=\frac{1}{4}(G\frac{m_1m_2}{r^2})$
Or $F'=\frac{1}{4}\times F$
So, option $(a)$ is correct.