Question

The gravitational force of attraction between two bodies at a certain distance is $10N$. If the distance between them is doubled, the force of attraction:

• A. decreases by $50\%$
• B. decreases by $75\%$
• C. increases by $50\%$
• D. increases by $75\%$

Answer 1

The correct option is B decreases by $75\%$

Let the two bodies have masses $m_1,m_2$
$F_G=\frac{G{m}_1{m}_2}{r^2}=10N$
When distance between them is doubled,
$F_G^{\prime }=\frac{G{m}_1{m}_2}{4r^2}=\frac{10}{4}$
$\therefore$$\frac{F_G^{\prime }}{F_G}=0.25$
So, force of attraction decreases by $75\%$.