Consider an equilateral prism (refractive index $\sqrt{2}$ ). A ray of light is incident on its one surface at a certain angle $i$. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to $\_\_\_\_$

A cylindrical tube $A B$ of length $l$, closed at both ends contains an ideal gas of 1 mol having molecular weight $M$. The tube is rotated in a horizontal plane with constant angular velocity $\omega$ about an axis perpendicular to $A B$ and passing through the edge at end $A$, as shown in the figure. If $P_A$ and $P_B$ are the pressures at $A$ and $B$ respectively, then (Consider the temperature is same at all points in the tube)

Electric field in a region is given by $\vec{E}=A x \hat{i}+B y \hat{j}$, where $A=10 \mathrm{~V} / \mathrm{m}^2$ and $B=5 \mathrm{~V} / \mathrm{m}^2$. If the electric potential at a point $(10,20)$ is 500 V , then the electric potential at origin is $\_\_\_\_$ V.

$X P Q Y$ is a vertical smooth long loop having a total resistance $R$ where $P X$ is parallel to $Q Y$ and separation between them is $l$. A constant magnetic field $B$ perpendicular to the plane of the loop exists in the entire space. A rod $C D$ of length $L(L>l)$ and mass $m$ is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is $\_\_\_\_$ $\mathrm{m} / \mathrm{s} .(\mathrm{g}=$ acceleration due to gravity)