An electron is projected in the direction of an electric field. Just after the projection of the electron:

$A$ small sphere of mass $m$ carrying a charge $q$ is hanging between two parallel plates by a string of length $L$ as shown in the figure. The time period of the pendulum is $T_0$. When the parallel plates are charged as shown,the time period changes to $T$. The ratio $T / T_0$ is equal to:

$A$ particle of mass $1 \, g$ and charge $-0.1 \, \mu C$ is projected from the ground with a velocity $10\sqrt{2} \, m/s$ at an angle of $45^o$ with the horizontal in a region having a uniform electric field $1 \, kV/cm$ in the horizontal direction. Acceleration due to gravity is $10 \, m/s^2$ in the vertical downward direction. Select the $INCORRECT$ statement.

$A$ small point mass carrying some positive charge is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options correctly describes the trajectory of the mass? (Curves are drawn schematically and are not to scale).

The figure shows the paths of three charged particles in a uniform electric field. Which particle has the highest charge-to-mass ratio?

$A$ uniform electric field,$\vec{E} = -400 \sqrt{3} \hat{y} \text{ NC}^{-1}$ is applied in a region. $A$ charged particle of mass $m$ carrying positive charge $q$ is projected in this region with an initial speed of $u = 2 \sqrt{10} \times 10^6 \text{ ms}^{-1}$. This particle is aimed to hit a target $T$,which is $5 \text{ m}$ away from its entry point into the field as shown schematically in the figure. Take $\frac{q}{m} = 10^{10} \text{ Ckg}^{-1}$. Then-
$(A)$ the particle will hit $T$ if projected at an angle $45^{\circ}$ from the horizontal
$(B)$ the particle will hit $T$ if projected either at an angle $30^{\circ}$ or $60^{\circ}$ from the horizontal
$(C)$ time taken by the particle to hit $T$ could be $\sqrt{\frac{5}{6}} \mu\text{s}$ as well as $\sqrt{\frac{5}{2}} \mu\text{s}$
$(D)$ time taken by the particle to hit $T$ is $\sqrt{\frac{5}{3}} \mu\text{s}$