In this problem, we are given two identical helium-filled balloons A and B, fastened to a weight of 5g by threads, which float in equilibrium. We are asked to calculate the charge on each balloon, assuming that they carry equal charges.


To calculate the charge on each balloon, we need to consider the equilibrium condition of the system. The weight of the thread and the weight of the balloons are balanced by the upward buoyant force acting on them. This buoyant force is due to the difference in density between the helium gas inside the balloons and the surrounding air.

We can use Coulomb's law to calculate the electrostatic force between the two balloons. Coulomb's law states that the electrostatic force between two charged objects is proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as F = k*q1*q2/d^2, where F is the electrostatic force, q1 and q2 are the charges on the two objects, d is the distance between them, and k is the Coulomb's constant.

Since the two balloons are identical, we can assume that they carry equal charges (let's call it q). Therefore, the electrostatic force between them is F = k*q^2/d^2. This electrostatic force must be balanced by the tension in the threads, which is equal to the weight of the weight (5g).

We can also write the buoyant force as Fbuoyant = (density of air - density of helium)*volume of the balloon*g, where g is the acceleration due to gravity. Since the two balloons are identical, their volumes and buoyant forces are equal.

Therefore, we can equate the electrostatic force and the tension in the threads as follows:

k*q^2/d^2 = 5g

We can also equate the buoyant force and the weight of the weight as follows:

(density of air - density of helium)*volume of the balloon*g = 5g

Solving these two equations simultaneously, we can find the charge on each balloon as follows:

q = sqrt((5g*d^2)/(k*volume of the balloon))


In summary, we can calculate the charge on each balloon by using Coulomb's law and the equilibrium conditions of the system. The charge on each balloon depends on the distance between them, the volume of the balloons, and the properties of the surrounding air and helium gas.