Question

Two object are placed at some distance, if their masses become two times and distance between them becomes half then value of new gravitational force will be :

• A. $4times$
• B. $8times$
• C. $16times$
• D. $32times$

Answer 1

The correct option is C $16times$

Newtons Law of Gravitation states that the force of gravity, $F_g$, between two particles of mass $m_1$ and

$m_2$ has a magnitude of
$F_g=\frac{G{m}_1{m}_2}{d^2}$
where r is the distance between the center of the two masses and G is the gravitational constant.
In this case, the masses are doubled and the radius is halved. So the Force becomes

$F_g=\frac{G{2m}_1{2m}_2}{{(\frac{d}{2})}^2}=16\frac{G{m}_1{m}_2}{d^2}$.
Hence, the new gravitational force will be 16 times more.