Question

If the masses of two objects are doubled, and the distance between them is halved, then the gravitational force acting between them becomes

• A. 4 times as before
• B. 2 times as before
• C. 16 times as before
• D. 3 times as before

Answer 1

The correct option is C 16 times as before

Accrding to Univarsal Law of Gravitation,
$F=\frac{G{m}_1{m}_2}{r^2}$
Doubling the mass, and reducing the radius to half,
$F^{\prime }=\frac{G{m}_1^{{}^{\prime }}{m}_2^{{}^{\prime }}}{(r^{{}^{\prime }}{)}^2}=\frac{G\left(2m_1\right)\left(2m_2\right)}{{\left(\frac{r}{2}\right)}^2}$
$=\frac{G{m}_1{m}_2\times 4}{\frac{r^2}{4}}$
$\frac{G{m}_1{m}_2\times 4}{\frac{r^2}{4}}$
$F^{{}^{\prime }}=16\frac{G{m}_1{m}_2}{r^2}$
$F^{{}^{\prime }}=16F$