two insulating small spheres are rubbed against each other and placed 1cm apart . if they attract each other with a force of 0.1 N , how many electrons were transferred from one sphere to the other while rubbing ?

Let N number of electrons get transferred from one sphere to the other.
Therefore, the charge on the two sphere is +Ne and -Ne.
Distance between the two charges, d = 1 cm = 0.01 m
The electrostatic force between the two charged sphere, F = 0.1 N
$$\begin{gathered} \frac{1}{4\pi {\in }_0}\frac{q_1{q}_2}{d^2}=0.1 \\ \frac{9\times {10}^9\times Ne\times Ne}{(0.01{)}^2}=0.1 \\ \frac{9\times {10}^9\times N^2\times e^2}{(0.01{)}^2}=0.1 \\ {N}^2=\frac{0.1\times (0.01{)}^2}{9\times {10}^9\times (1.6\times {10}^{-19}{)}^2}=4.34\times {10}^{22} \\ N=\sqrt{4.34\times {10}^{22}}=2.08327\times {10}^{11} \end{gathered}$$