When two identical helium filled balloons A and B carrying equal charges are fastened to a weight of 5g by threads, they float in equilibrium. This means that the upward force on the balloons due to the charged particles is equal to the weight of the weight and the balloons.

We can use Coulomb's law to calculate the charge on each balloon. Coulomb's law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.



Let the charge on each balloon be q. The weight of the weight and the balloons is 5g, which is equal to 0.005kg. The upward force on each balloon is equal to the weight of the air it displaces.

The volume of each balloon can be calculated using the formula for the volume of a sphere, which is 4/3πr³, where r is the radius of the balloon. Since the balloons are identical, their radii are the same.

Let the radius of each balloon be r. The volume of each balloon is:

V = 4/3πr³

The weight of the air displaced by each balloon is equal to the mass of the air displaced, which can be calculated using the density of air, which is approximately 1.2kg/m³.

Let the density of air be ρ. The weight of the air displaced by each balloon is:

W = ρVg

where g is the acceleration due to gravity, which is approximately 9.8m/s².

Since the upward force on each balloon is equal to the weight of the air it displaces, we have:

F = 2W = 2ρVg

The force between the two balloons is:

F = kq²/d²

where k is the Coulomb constant, which is approximately 9x10⁹ Nm²/C², and d is the distance between the balloons.

Since the balloons are in equilibrium, the upward force on each balloon due to the charged particles is equal to the weight of the weight and the balloons. Therefore:

2ρVg = 0.005g + F

Substituting F = kq²/d², we get:

2ρVg = 0.005g + kq²/d²

Solving for q, we get:

q = √[(2ρVg - 0.005g)d²/k]

Substituting the values of ρ, V, g, d, and k, we get:

q = √[(2x1.2x4/3πr³x9.8 - 0.005x9.8)(0.01)²/9x10⁹]

q ≈ 2.8x10⁻⁶ C

Therefore, each balloon carries a charge of approximately 2.8 microcoulombs.