Question

When the mass of one of the two bodies is doubled the gravitational force between them increases by ________ times.

Answer 1

The gravitation force between two bodies given as-

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

$F$; force between them

$G$; gravitational constant$(6.67\times {10}^{-11}N{m}^{2}k{g}^{-2})$

$m_1\text{and}{m}_2$; masses of the two object

$r$; distance between them

Now suppose one mass becomes doubled-

$m_1^{\prime }=2m_1$

then force-

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

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

$\Rightarrow F^{\prime }=2F$

So force becomes double when one mass is doubled.