If the distance between two particles is halved, the gravitational force increases by:a.Three timesb.Eight timesc.Four timesd.Two times

The gravitational force between two particles is given by Newton's law of universal gravitation:

F = G * (m1 * m2) / r^2

where: F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the particles, r is the distance between the particles.

If the distance between the particles is halved, the new distance is r/2. Substituting this into the equation gives the new force F':

F' = G * (m1 * m2) / (r/2)^2 = G * (m1 * m2) / (r^2 / 4)

This simplifies to:

F' = 4 * G * (m1 * m2) / r^2 = 4F

So, if the distance between two particles is halved, the gravitational force increases by four times. Therefore, the correct answer is c. Four times.