$A$ particle of charge $Q$ and mass $m$ travels through a potential difference $V$ from rest. The final momentum of the particle is

$A$ thin conducting spherical shell of radius $R$ has a charge $q$. Another charge $Q$ is placed at the center of the shell. The electrostatic potential at a point $P$ at a distance $R/2$ from the center of the shell is:

Two charges $q_1$ and $q_2$ are fixed at points $A$ and $B$ respectively, separated by a distance of $30 \text{ cm}$. $A$ third charge $q_3$ is moved along a circular path of radius $40 \text{ cm}$ from point $C$ to point $D$. If the difference in potential energy due to the movement of $q_3$ from $C$ to $D$ is $q_3 K / (4 \pi \epsilon_0)$, find the value of $K$. (Given: $AC = 40 \text{ cm}$, $AB = 30 \text{ cm}$, $AD = 40 \text{ cm}$)

Two point charges of $1 \text{ nC}$ and $2 \text{ nC}$ are placed at two corners of an equilateral triangle of side $3 \text{ cm}$. The work done in bringing a charge of $3 \text{ nC}$ from infinity to the third corner of the triangle is . . . . . . $\mu\text{J}$. $( \frac{1}{4\pi\epsilon_{0}} = 9 \times 10^{9} \text{ N.m}^{2}/\text{C}^{2} )$

$A$ particle of mass $m$ and charge $q$ is accelerated through a potential difference of $V$ volt. Its energy will be:

$A$ charge of $5\,C$ is given a displacement of $0.5\,m$. The work done in the process is $10\,J$. The potential difference between the two points will be.......$V$