Introduction:
Gravitational force is the force of attraction between two objects with mass. The force of gravity between two objects depends on their masses and the distance between them. In this scenario, we have two particles placed at a certain distance, and we need to determine how the gravitational force between them changes when the mass of each particle is doubled while keeping the distance unchanged.

Explanation:
To understand how the gravitational force changes, we need to consider Newton's law of universal gravitation. According to this law, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

1. Initial situation:
Let's assume the initial masses of the two particles are m1 and m2, with a distance between them given by d. Therefore, the initial gravitational force between them can be calculated as:
F1 = G * (m1 * m2) / d^2

2. Doubling the mass:
Now, if we double the mass of each particle, the new masses become 2m1 and 2m2, respectively. However, the distance between them remains the same (d).

3. Calculating the new gravitational force:
To determine the new gravitational force, let's substitute the new masses into the formula:
F2 = G * ((2m1) * (2m2)) / d^2

Simplifying this expression, we get:
F2 = 4 * (G * (m1 * m2) / d^2)

4. Comparison:
Comparing the initial force (F1) and the new force (F2), we can see that the new force (F2) is four times greater than the initial force (F1).

Conclusion:
When the mass of each particle is doubled while keeping the distance between them unchanged, the gravitational force between them increases by a factor of four. This can be explained by the direct proportionality between the gravitational force and the product of the masses. Doubling the mass of each particle results in a fourfold increase in the product of their masses, leading to a fourfold increase in the gravitational force between them.

let mass of first particle = m1and of particle of 2nd = m2we know d1=d2=dso F1= m1 m2 /dover here F2 = 2m1 X 2m2/dF2 = 4 X m1m2/dbut (1) says F1 = m1 m2 /dF2=4 X F1So force is 4 times greater than the older force