Question

The gravitational force between two objects is $F$. If the mass of one of the objects is doubled and the distance between the objects is halved, then the gravitational force would become

• A. $4F$
• B. $\frac{F}{4}$
• C. $8F$
• D. $\frac{F}{8}$

Answer 1

The correct option is C $8F$

Let $m_1$ and $m_2$ be the mass of the two object and $r$ be the distance between them. Then we know from the Universal law of gravitation that

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

Now, mass of one of the objects is doubled and the distance between the objects is halved. So,

$m_1^{\prime }=2m_1,r^{\prime }=\frac{r}{2}$

The new force will be,

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

$F^{\prime }=\frac{G\left(2m_1\right)m_2}{{\left[\frac{r}{2}\right]}^2}$

$\Rightarrow F^{\prime }=8\times \frac{G{m}_1{m}_2}{r^2}=8F$