Two bodies of equal masses are some distance apart. If $20 \%$ of mass is transferred from the first body to…
Two bodies of equal masses are some distance apart. If $20 \%$ of mass is transferred from the first body to the second body, then the gravitational force between them
increase by $4 \%$
increase by $14 \%$
decreases by $4 \%$
decreases by $14 \%$
Solution
(c) Initially force,
$
F_1=\frac{G m^2}{r^2}
$
When $20 \%$ mass is transferred from one body to another, then their masses are
$
m_1=\frac{80}{100} m \text { and } m_2=\frac{120}{100} m
$
So, force is finally
$
F_2=\frac{G m^2}{r^2} \times\left(\frac{24}{25}\right)
$
Hence, reduction in $F_2$ is $\frac{F_1-F_2}{F_1} \times 100 \%=-4 \%$