The distance between the two point masses $m_{1}$ and $m_{2}$ is d. Now, the distance between them is reduced by two-thirds, Calculate by which factor new gravitational force would be change?

It increases by a factor of

9

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It increases by a factor of

\frac{4}{9}

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It increases by a factor of

3

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It decreases by factor of

9

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It decreases by a factor of

3

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Solution

The correct option is A It increases by a factor of $9$
Given that the distance reduces by two-thirds, means that the new distance is
$d_{1} = d - (\frac{2}{3} \times d) = \frac{d}{3}$
Therefore new force is $F_{1} = G \frac{m_{1} m_{2}}{d_{1}^{2}} = 9 G \frac{m_{1} m_{2}}{d^{2}} = 9 F$
Hence option A is correct.

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The distance between the two point masses m1 and m2 is d. Now, the distance between them is reduced by two-thirds, Calculate by which factor new gravitational force would be change?

The correct option is A It increases by a factor of 9Given that the distance reduces by two-thirds, means that the new distance isd1=d−(23×d)=d3Therefore new force is F1=Gm1m2d21=9Gm1m2d2=9FHence option A is correct.

The distance between the two point masses $m_{1}$ and $m_{2}$ is d. Now, the distance between them is reduced by two-thirds, Calculate by which factor new gravitational force would be change?