Question

If the distance between two bodies is increased by $25$%, then the percentage change in the gravitational force:

• A. decreases by $36$%
• B. increases by $36$%
• C. increases by $64$%
• D. decreases by $64$%

Answer 1

The correct option is A decreases by $36$%

$F_2/F_1=\left(d_1{)}^2/\right(d_2{)}^2$
$d_2=d_1+\left(d_1\right)/4$
Substituting the values of $d_2$ and $d_1$
$F_2/F_1=16/25$
Calculating $dF/F$
$dF/F=F_2-F_1/F_1=-9/25$
$dF/F\times 100=-36\%$
Therefore the force decreases by $36\%$