The gravitational force of attraction between two objects is $x$. Keeping the masses of the objects unchanged, if the distance between the objects is halved, then the magnitude of gravitational force between them will
(a) $x/4$
(b) $x/2$
(c) $2x$
(d) $4x$

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, $x=G\frac{m_1m_2}{r^2}$

Here, $x\rightarrow$ 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 distance between the two objects is halved, then it will become $\frac{r}{2}$.

Then, force of attraction, $x'=G\frac{m_1m_2}{(\frac{r}{2})^2}$

Or $x'=(G\frac{m_1m_2}{(\frac{r^2}{4})})$

Or $x'=4\times x$

So, option $(d)$ is correct.

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Updated on: 10-Oct-2022

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