Two spheres having the same radius and mass are suspended by two strings of equal length from the same point in such a way that their surfaces touch each other. On depositing a charge of $2 \times 10^{-6} \ C$ on them,they repel each other such that in equilibrium,the angle between their strings becomes $60^{\circ}$. If the distance from the point of suspension to the center of the sphere is $10 \ cm$,find the mass of each sphere. $(k = 9 \times 10^9 \ SI, g = 10 \ ms^{-2})$. (in $kg$)

Why is Coulomb's law associated with Newton's $3^{rd}$ law?

Two point charges $+9e$ and $+e$ are placed at a distance of $16\, cm$ from each other. Where should a third charge $q$ be placed between them so that the system remains in equilibrium?

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting,massless strings of same length. At equilibrium,the angle between the strings is $\alpha$. The spheres are now immersed in a dielectric liquid of density $\rho_l = 800 \ kg \ m^{-3}$ and dielectric constant $K = 21$. If the angle between the strings remains the same after the immersion,then
$(A)$ electric force between the spheres remains unchanged
$(B)$ electric force between the spheres reduces
$(C)$ mass density of the spheres is $840 \ kg \ m^{-3}$
$(D)$ the tension in the strings holding the spheres remains unchanged

Two small balls,each having mass $m$ and charge $q$,are suspended from a common point by insulating strings of length $L$ as shown in the figure. Assuming $\theta$ is very small such that $\tan \theta \approx \sin \theta$,find the value of $x$ at equilibrium.

Coulomb's law for electrostatic force between two point charges and Newton's law for gravitational force between two stationary point masses,both have inverse-square dependence on the distance between the charges and masses respectively.
$(a)$ Compare the strength of these forces by determining the ratio of their magnitudes $(i)$ for an electron and a proton and $(ii)$ for two protons.
$(b)$ Estimate the accelerations of electron and proton due to the electrical force of their mutual attraction when they are $1 \mathring A \left( = 10^{-10} \, m \right)$ apart? $\left( m_{p} = 1.67 \times 10^{-27} \, kg, m_{e} = 9.11 \times 10^{-31} \, kg \right)$