An electron enters in high potential region ${V_2}$ from lower potential region ${V_1}$ then its velocity

A block of mass $m$ moving with speed $v$ compresses a spring through distance $x$ before its speed is halved. What is the value of spring constant ?

A charged particle $q$ is shot towards another charged particle $Q$ which is fixed, with a speed $v$. It approaches $Q$ upto a closest distance $r$ and then returns. If $q$ were given a speed $2v$, the closest distances of approach would be

In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_A=1$, within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_A=k r$, where $k$ is positive. In the spherical shell $B$ of outer radius $r_B$, the electrostatic charge density varies as $\rho_{\bar{B}}=\frac{2 k}{r}$. Assume that dimensions are taken care of. All physical quantities are in their $SI$ units.

Which of the following statement($s$) is(are) correct?

Four charges are arranged at the corners of a square $ABCD$ of side $d$, as shown in Figure

$(a)$ Find the work required to put together this arrangement.

$(b)$ A charge $q_{0}$ is brought to the centre $E$ of the square, the four charges being held fixed at its corners. How much extra work is needed to do this?

As per this diagram a point charge $ + q$ is placed at the origin $O$. Work done in taking another point charge $ - Q$ from the point $A$ [co-ordinates $(0,\,a)$] to another point $B$ [co-ordinates $(a, 0)$] along the straight path $AB$ is