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  4. If the distance between the sun and the earth is increased by three times then attraction between two will

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Q. If the distance between the sun and the earth is increased by three times then attraction between two will

ManipalManipal 2008Gravitation

Solution:

$F=\frac{G m_{1} m_{2}}{r^{2}}$
and $F'=\frac{G m_{1} m_{2}}{(3 r)^{2}}=\frac{F}{9}$
$\therefore \%$ decrease in $F=\left(\frac{F-F'}{F}\right) \times 100$
$=\frac{8}{9} \times 100$
$=89 \%$
Thus, attraction force between sun and earth is decreased by $89\%$.