Question

If the mass of two bodies become double & also the distance between them becomes twice the gravitational force will be :

• A. Double
• B. half
• C. 4
• D. Remain same

Answer 1

The correct option is D Remain same

Gravitational force can be given as [Initially], $F=\frac{G{m}_1{m}_2}{d^2}$

If $d^{\prime }=2d,m_1^{\prime }=2m$ and $m_2^{\prime }=2m_2$

Then ,

Gravitational force can be given as [Finally], $F^{\prime }=G\frac{m_1^{\prime }{m}_2^{\prime }}{d^{\prime 2}}=G\frac{2m_1\times 2m_2}{(2d{)}^2}$

$\Rightarrow F^{\prime }=G\frac{4m_1{m}_2}{4d^2}=\frac{G{m}_1{m}_2}{d^2}=F$

$\therefore F^{\prime }=F$

So, the gravitational force will be same in both the case.

Hence the correct option is $\left(D\right)$