Question

If the distance between the sun and the earth is increased to three times then the attraction between the two will

• A. Remains constant
• B. Decrease by 63%
• C. Decrease by 83%
• D. Decrease by 89%

Answer 1

The correct option is D Decrease by 89%

$F=\frac{G{m}_1{m}_2}{r^2}\Rightarrow F\propto \frac{1}{r^2}$
$r(\uparrow )\Rightarrow F(\downarrow )$
$F=\frac{G{M}_s{M}_e}{r^2}$
$F^{\prime }=\frac{G{M}_s{M}_e}{(3r{)}^2}=\frac{G{M}_s{M}_e}{9r^2}$
$F^{\prime }=\frac{F}{9}$
$\%change\Rightarrow \left(\frac{F^{\prime }-F}{F}\right)\times 100$
$=\left(\frac{\frac{F}{9}-F}{F}\right)\times 100$
$=-\frac{8}{9}\times 100$
= 89%.