# T w o <mtext>&#xA0;</mtext> o b j e c t s , <mtext>&#xA0;</m

Two objects, with masses ${m}_{1}$ and ${m}_{2}$, attract each other with force $F$. If the mass of ${m}_{1}$ increased by a factor of two then the new gravitational force would be:
F/4
2 F
4 F
F/2

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Step 1
Write the mathematical expression for the gravitational force between two masses.
$F=\frac{G{m}_{1}{m}_{2}}{{R}^{2}}$
Here,
The distance between the two objects is "R"
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Step 2
When the mass increased by a factor of two.
Write the mathematical expression for the gravitational force between two masses.
${F}^{\prime }=\frac{G\left(2{m}_{1}\right){m}_{2}}{{R}^{2}}\phantom{\rule{0ex}{0ex}}=2\left(\frac{G{m}_{1}{m}_{2}}{{R}^{2}}\right)\phantom{\rule{0ex}{0ex}}2F$
Hence, the new gravitational force becomes 2F