The gravitational force between two point masses m and M separated by a distance d is F. Now a point mass ‘3m’ is placed next to m so that the total force on M is XF. What must be the value of X?

Gravitational force between the two particles can be given as:
$\text{F}=\frac{\text{GmM}}{{\text{d}}^{\text{2}}}$ 
Now a particle of mass '3m' is placed close to the particle m, so the total mass will be:
$\mathrm{m} + 3\mathrm{m} = 4\mathrm{m}$

The new vaue of the force exerted on the mass M can be given as:

${\text{F}}^{\text{1}}=4\frac{\text{GmM}}{{\text{d}}^{\text{2}}}$

From the first equation, we can write,

${\text{F}}^{\text{1}}=4\text{F}$
The total force on M is 4F.
Therefore, the value of X will be 4.