A wooden block performs $SHM$ on a frictionless surface with frequency, $v_0$. The block carries a charge $+Q$ on its surface. If now a uniform electric field $\vec{E}$ is switched-on as shown, then the $SHM$ of the block will be

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density $\lambda$ are kept parallel to each other. In their resulting electric field, point charges $q$ and $- q$ are kept in equilibrium between them. The point charges are confined to move in the $x$ direction only. If they are given a small displacement about their equilibrium positions, then the correct statement$(s)$ is(are)

A charged particle of mass $m$ and charge $q$ is released from rest in a uniform electric field $E.$ Neglecting the effect of gravity, the kinetic energy of the charged particle after ‘$t$’ second is

Two identical positive charges are fixed on the $y$ -axis, at equal distances from the  origin $O$. A particle with a negative charge starts on the $x$ -axis at a large distance  from $O$, moves along the $+ x$ -axis, passes through $O$ and moves far away from $O$. Its acceleration $a$ is taken as positive in the positive $x$ -direction. The particle’s  acceleration a is plotted against its $x$ -coordinate. Which of the following best represents  the plot?

In Millikan's oil drop experiment, a charged drop falls with terminal velocity $V$. If an electric field $E$ is applied in vertically upward direction then it starts moving in upward direction with terminal velocity $2V$.If magnitude of electric field is decreased to $\frac{E}{2}$, then terminal velocity will become