Question

If $F$ is the force between two bodies of masses $m_1$ and $m_2$ at a certain separation, then what is the force between $\sqrt{5}{m}_1$ and $\sqrt{3}{m}_2$ at the same separation?

• A. $\sqrt{5}F$
• B. $\frac{F}{\sqrt{15}}$
• C. $\sqrt{15}F$
• D. $F$

Answer 1

The correct option is C

$\sqrt{15}F$

Force between bodies of masses $m_1$ & $m_2$ separated by a distance $r$:
$F=G\frac{m_1{m}_2}{r^2}$ $\cdots \left(1\right)$
Force between bodies of masses $\sqrt{5}{m}_1\&\sqrt{3}{m}_2$ at the same separation $r$:
$F^{\prime }=G\frac{\sqrt{5}{m}_1\times \sqrt{3}{m}_2}{r^2}$ $\cdots \left(2\right)$
Dividing eqn (1) by eqn (2)
$\frac{F}{F^{\prime }}=\frac{1}{\sqrt{15}}\Rightarrow F^{\prime }=\sqrt{15}F$
Hence, force between $\sqrt{5}{m}_1$ and $\sqrt{3}{m}_2$ is $\sqrt{15}F$