Question

If F is the force between two bodies of masses $m_1$ and $m_2$ at certain separation, then the force between $\sqrt{2}{m}_1$ and $\sqrt{3}{m}_2$ at same separation is: _______

• A. $\sqrt{6}F$
• B. $\sqrt{26}F$
• C. $6F$
• D. $\sqrt{216}F$

Answer 1

The correct option is A $\sqrt{6}F$

F=$\frac{G{m}_1{m}_2}{r^2}$

Now the force between the mass $\sqrt{2}{m}_1$ and $\sqrt{3}{m}_2$ at same separation is $F^{\prime }=\frac{G\sqrt{2}{m}_1\sqrt{3}{m}_2}{r^2}=\sqrt{6}\frac{G{m}_1{m}_2}{r^2}=\sqrt{6}F$

[$\because F=\frac{G{m}_1{m}_2}{r^2}$]