Recall, Newton's gravitational law states that any particle of matter in the universe attracts any other particle with a force varying directly as the product of their masses and inversely as the square of the distance between them. It is expressed as
F = Gm1m2/r^2
where
F is the force in Newton
G is gravitational constant = 6.673 x 10^-11 Nm^2/kg^2
m1 and m2 are the masses in kg
r is the distance in meters
From the information given,
r = 1.5
acceleration = 2cm^2/s
Recall, 100 cm = 1m
2 cm = 2/100 = 0.02m
Thus,
acceleration = 0.02m/s^2
Since the masses are identical, then m1 = m2
Each of them is accelerating at 0.02m/s^2
Recall,
Force = mass x acceleration
Force = m1 x 0.02 = 0.02m1 N
By substituting the given values into the formula, we have
0.02m1 = (6.673 x 10^-11 x m1 x m1)/1.5^2
m1 on the left cancels out one m1 on the right. It becomes
0.02 = (6.673 x 10^-11 x m1)/1.5^2
By crossmultiplying,
0.02 x 1.5^2 = 6.673 x 10^-11 x m1
0.045 = 6.673 x 10^-11 x m1
m1 = 0.045/6.673 x 10^-11
m1 = 6.74 x 10^8 kg
The mass of each ball is 6.74 x 10^8 kg