Consider the following charged suspended ball system. If $\alpha < \beta$,then out of the following statements,which can be true at equilibrium? :-
$(a) Q_1 > Q_2, m_1 < m_2$
$(b) Q_1 > Q_2, m_1 > m_2$
$(c) Q_1 < Q_2, m_1 = m_2$
$(d) Q_1 < Q_2, m_1 > m_2$

The ratio of the forces between two small spheres with constant charge $(a)$ in air and $(b)$ in a medium of dielectric constant $K$ is:

Two point charges $A$ and $B$ with magnitudes $+4q$ and $-4q$ are placed along a line separated by a distance $r$. The force acting between them is $F$. If $25\%$ of the charge from point $A$ is transferred to point $B$,the force between the charges now becomes:

Two charges $q_1$ and $q_2$ are placed in vacuum at a distance $d$ and the force acting between them is $F$. If a medium of dielectric constant $4$ is introduced around them,the force now will be

The acceleration of an electron due to the mutual attraction between the electron and a proton when they are $1.6 \; \mathring{A}$ apart is,$(m_{e} \simeq 9 \times 10^{-31} \; kg, e = 1.6 \times 10^{-19} \; C)$. (Take $\frac{1}{4 \pi \varepsilon_{0}} = 9 \times 10^{9} \; Nm^{2} C^{-2}$)

$A$ point charge $q_1 = 4 q_0$ is placed at the origin. Another point charge $q_2 = -q_0$ is placed at $x = 12 \, cm$. The charge of a proton is $q_0$. $A$ proton is placed on the $x$-axis such that the net electrostatic force on it is zero. In this situation,the position of the proton from the origin is $.......... \, cm$.