How many electrons should be removed from a coin of mass $1.6 \,g$,so that it may float in an electric field of intensity $10^9 \,N/C$ directed upward?

$A$ charged cork ball having mass $1 \text{ g}$ and charge $q$ is suspended on a light string in a uniform electric field as shown in the figure. The ball is in equilibrium at $\theta=37^{\circ}$,when the value of the electric field is $E=(3 \hat{i}+5 \hat{j}) \times 10^5 \text{ NC}^{-1}$. (Assume $T$ as tension in the string.) Which of the following options are correct? (Given,$\sin 37^{\circ}=0.60$ and $g=10 \text{ ms}^{-2}$)

$A$ simple pendulum has a bob with mass $m$ and charge $q$. The pendulum string has negligible mass. When a uniform and horizontal electric field $\vec{E}$ is applied,the final tension in the string changes. The final tension in the string,when the pendulum attains an equilibrium position,is . . . . . . . ($g$: acceleration due to gravity)

$A$ particle of mass $m$ and charge $q$ is thrown perpendicular to an electric field of intensity $E$ with an initial velocity $v$. The particle moves a distance $x$ perpendicular to the field and a distance $y$ along the direction of the field. If $y = \alpha x^{2}$,then $\alpha$ is given by:

$A$ mass $m = 20\,g$ has a charge $q = 3.0\,mC$. It moves with a velocity of $20\,m/s$ and enters a region of electric field of $80\,N/C$ in the same direction as the velocity of the mass. The velocity of the mass after $3\,s$ in this region is.......$m/s$.

Calculate the work done by the electrostatic force on an electron moving in a circular orbit around the nucleus.