Question

What will happen to the gravitational force between two bodies if the mass of
one body is doubled and distance between them is halved?​

Answer 1

The gravitational force between two bodies is given by:-

$\sf F=G\dfrac{m_1m_2}{d^2}$

G is the gravitational constant

m_1\ and\ m_2m1 and m2 are masses

d is the distance between masses

If mass of each body is doubled and the distance between them is halved such that,

m_1'=m_2'=2m

$\sf d'=\dfrac{d}{2}$

New gravitational force is given by :

$\sf F'=G\dfrac{m_1'm_2'}{d^2}$

$\sf F'=G\dfrac{(2m)^2}{(d/2)^2}$

$\sf F'=16\times G\dfrac{m_1m_2}{r^2}$

$\sf F'=16\times F$

So, the mass of each body is doubled and the distance between them is halved, then the force between them will be 16 time the initial force.