Question

Suppose gravitational force between two masses were to be given by $F=k\frac{\sqrt{m_1{m}_2}}{d^3}$ where k is some constant, two equal masses attract each other with a certain force when the distance is d. If each of the masses is doubled, than what value the distance between them must be maintained for the force to remain the same as earlier?

• A. $\sqrt[3]{33d}$
• B. $\sqrt[13]{133d}$
• C. $\sqrt[13]{132d}$
• D. $\sqrt[3]{32d}$

Answer 1

The correct option is D $\sqrt[3]{32d}$

$F=\frac{k\sqrt{m_1^{\prime }{m}_2^{\prime }}}{d^3}$ (given) [k=constant]

Now, $F^{\prime }=\frac{k\sqrt{m_1^{\prime }{m}_2^{\prime }}}{d_3^{\prime }}$

$d^{\prime }$=? for $F^{\prime }$=F, $m_1^{\prime }=2m_1$, $m_2^{\prime }=2m_2$

$\therefore F=\frac{k\sqrt{{2m}_1{m}_2}}{d^{\prime 3}}=>\frac{k\sqrt{m_1{m}_2}}{d^3}=\frac{2k\sqrt{m_1{m}_2}}{d^{\prime 3}}=>d^{\prime 3}=2d^3=>d^{\prime }=\sqrt[3]{32d}$