The resistance across $M$ and $N$ in the given figure is

Consider a block of conducting material of resistivity ' $\rho$ ' as described. Current ' $I$ ' enters at ' $A$ ' and leaves from ' $D$ '. We apply the superposition principle to find the voltage ' $\Delta V$ ' developed between ' $B$ ' and ' $C$ '. The calculation is done in the following steps:
$(i)$ Take current ' $I$ ' entering from ' $A$ ' and assume it to spread over a hemispherical surface in the block.
(ii) Calculate the field $E(r)$ at distance ' $r$ ' from $A$ by using Ohm's law $E = \rho j$,where $j$ is the current per unit area at ' $r$ '.
(iii) From the ' $r$ ' dependence of $E(r)$,obtain the potential $V(r)$ at $r$.
(iv) Repeat $(i)$,(ii),and (iii) for current ' $I$ ' leaving ' $D$ ' and superpose results for ' $A$ ' and ' $D$ '.
For current entering at $A$,the electric field at a distance ' $r$ ' from $A$ is:

If $E, M, J$ and $G$ respectively denote energy,mass,angular momentum,and universal gravitational constant,the quantity which has the same dimensions as the dimensions of $\frac{E J^2}{M^5 G^2}$ is:

Suppose $A$ and $B$ are two points on the line $2x-y+3=0$ and $P(1,2)$ is a point such that $PA=PB$. Then,the mid-point of $AB$ is

In a compound,$C$,$H$,and $N$ atoms are present in the ratio $9 : 1 : 3.5$ by weight. The molecular weight of the compound is $108$. Its molecular formula is:

Liquid $X$ is used in a bubble chamber to detect neutral mesons and gamma photons. Then,$X$ is