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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
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Verified Answer
The correct answer is:
decreases by $4 \%$
(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 $\frac{F_1-F_2}{F_1} \times 100 \%=-4 \%$
$$
F_1=\frac{G m^2}{r^2}
$$
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 $\frac{F_1-F_2}{F_1} \times 100 \%=-4 \%$
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