Introduction:
When two insulating small spheres are rubbed against each other, they can transfer charge from one sphere to the other. This transfer of charge occurs due to the movement of electrons. In this scenario, we are given that the spheres attract each other with a force of 0.1N and are placed 96cm apart. We need to calculate the number of electrons transferred from one sphere to the other during rubbing.

Step 1: Understanding the force of attraction:
The force of attraction between the spheres can be calculated using Coulomb's law. According to Coulomb's law, the force between two charged objects is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, it can be represented as:

F = k * (q1 * q2)/r^2

Where:
F is the force of attraction,
k is the electrostatic constant,
q1 and q2 are the charges on the spheres,
r is the distance between the spheres.

Step 2: Calculating the charge on the spheres:
Since the spheres are insulating, the charge on each sphere is an integer multiple of the elementary charge, e. Let's assume that the number of electrons transferred from one sphere to the other is n.

Therefore, the charge on one sphere, q1, can be given as:
q1 = n * e

The charge on the other sphere, q2, can be given as:
q2 = -n * e (since opposite charges attract)

Step 3: Substituting values and solving the equation:
We are given that the force of attraction between the spheres is 0.1N and the distance between them is 96cm. The electrostatic constant, k, is a known constant.

Plugging in these values in Coulomb's law equation, we get:
0.1 = k * ((n * e) * (-n * e))/(0.96)^2

Step 4: Solving for n:
We can rearrange the equation to solve for n:
n^2 * e^2 = (0.1 * (0.96)^2)/(k * e^2)

Simplifying the equation further, we get:
n^2 = (0.1 * (0.96)^2)/(k * e^4)

Taking the square root of both sides, we get:
n = √((0.1 * (0.96)^2)/(k * e^4))

Step 5: Calculating the value of n:
Now, we can substitute the values of the known constants into the equation and calculate the value of n.

Finally, we can determine the number of electrons transferred from one sphere to the other during rubbing by substituting the value of n into the equation:
Number of electrons transferred = n * elementary charge

Conclusion:
By following the above steps and calculating the value of n, we can determine the number of electrons transferred from one sphere to the other during rubbing.