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

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$\frac{F}{4}$

$\frac{F}{2}$

answer is A.

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Detailed Solution

We know that

$F_{1} = \frac{{Gm}_{1} m_{2}}{r_{1}^{2}}$

$m_{1}^{1} = \frac{m_{1}}{2} m_{2}^{1} = \frac{m_{2}}{2}$

And $r_{1}^{2} = r_{1}$

Then $F^{|} = \frac{{Gm}_{1}^{|} {m_{2}}^{|}}{r^{|}}$

$F^{|} = G \cdot \frac{m_{1}}{2} \times \frac{m_{2}}{2} \times \frac{1}{r}$

$F^{|} = \frac{{Gm}_{1} m_{2}}{{4r}_{1}^{2}} = \frac{F}{4} [∵ \frac{{Gm}_{1} m_{2}}{r_{1}^{2}} = F]$

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