Physics

Two infinite planes each with uniform surface charge density $+\sigma$ $$ are kept in such a way that the angle between them is ${30}^{?}$ ${}^{}$ . The electric field in the region shown between them is given by:

The dimension of $\frac{{\mathrm{B}}^2}{2{\mu }_0}$ , where $\mathrm{B}$ is magnetic field and ${\mu }_0$  is the magnetic permeability of vacuum, is

A polarizer-analyser set is adjusted such that the intensity of light coming out of the analyser is just $10\mathrm{\%}$ $$ of the original intensity. Assuming that the polarizer-analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero is

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4 $\mathrm{k}\mathrm{g}$ . (the coordinates of the same are shown in figure) are:

A box weighs $196\mathrm{N}$ on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take $\mathrm{g}=10{\mathrm{m}\mathrm{s}}^{-2}$ at the north pole and the radius of the earth $=6400\mathrm{k}\mathrm{m}$  )

A thermodynamic cycle $xyzx$ is shown on a $V-T$  diagram. The P-V diagram that best describes this cycle is: (diagrams are schematic and not to scale)

A particle of mass $$ $m$ is fixed to one end of a light spring having force constant $$ $k$ and unstretched length $\mathcal{l}$ $$ . The other end is fixed. The system is given an angular speed $\omega$ $$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, $T_1$ and $T_2$ . The temperature of the hot reservoir of the first engine is $T_1$ and the temperature of the cold reservoir of the second engine is $T_2$ . $T$ is temperature of the sink of first engine which is also the source for the second engine. How is $T$ related to $T_1$ and $T_2$ , if both the engines perform equal amount of work?

A planar loop of wire rotates in a uniform magnetic field. Initially, at $t=0$ , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of $10\mathrm{s}$  about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

A thermodynamic cycle $xyzx$ is shown on a $V-T$  diagram. The P-V diagram that best describes this cycle is: (diagrams are schematic and not to scale)