Question

If the gravitational force between two spheres is $400N$, and the distance between them is doubled, the force will be ____________

• A. $400N$
• B. $200N$
• C. $100N$
• D.
  $40N$

Answer 1

The correct option is C $100N$

Given, $r_2=2r_1$
From Newtons law of Gravitation,
$F_1=\frac{G{M}_1{M}_2}{(r_1{)}^2}$ and $F_2=\frac{G{M}_1{M}_2}{(r_2{)}^2}$
​or, $\frac{F_1}{F_2}=\frac{G{M}_1{M}_2}{(r_1{)}^2}\times \frac{(r_2{)}^2}{G{M}_1{M}_2}$
or, $\frac{F_1}{F_2}=\frac{(r_2{)}^2}{(r_1{)}^2}$
or, $\frac{F_1}{F_2}=\frac{(2r_1{)}^2}{(r_1{)}^2}$
or, $F_2=\frac{F_1}{4}=\frac{400}{4}=100N$