Physics

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from ${\tau }_1$ to ${\tau }_2$ . If $\frac{C_p}{C_v}=\gamma$ for the gas then a good estimate for $\frac{{\tau }_2}{{\tau }_1}$  is given by

The electric field of a plane electromagnetic wave is given by $\stackrel{?}{\mathrm{E}}={\mathrm{E}}_0\frac{\stackrel{\mathrm{ˆ}}{\mathrm{i}}+\stackrel{\mathrm{ˆ}}{\mathrm{j}}}{\sqrt[]{2}}\mathrm{c}\mathrm{o}\mathrm{s}?(\mathrm{k}\mathrm{z}+\omega \mathrm{t})$

At $\mathrm{t}=0$ , a positively charged particle is at the point $(x,y,z)=\left(\mathrm{0,0},\frac{\pi }{k}\right)$ . If its instantaneous velocity at $(t=0)$ is $v_0\hat{k}$ , the force acting on it due to the wave is:

A mass of $10\mathrm{k}\mathrm{g}$ is suspended by a rope of length $4\mathrm{m}$ , from the ceiling. A force $F$ is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of ${45}^{?}$ with the vertical. Then $\mathrm{F}$ equals: (Take $\mathrm{g}=10{\mathrm{m}\mathrm{s}}^{-2}$  and the rope to be massless)

What is the period of circular motion?

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are $6.4\mathrm{c}\mathrm{m}$ and $4.8\mathrm{c}\mathrm{m}$ , respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is

The activity of a radioactive sample falls from $700{\mathrm{s}}^{-1}$ to $500{\mathrm{s}}^{-1}$  in 30 minutes. Its half life is close to

The figure gives experimentally measured $B$ vs $\mathrm{H}$  variation in a ferromagnetic material. The retentivity, co-ercivity and saturation, respectively, of the material are

In a Young's double slit experiment, the separation between the slits is $0.15\mathrm{m}\mathrm{m}$ . In the experiment, a source of light of wavelength $589\mathrm{n}\mathrm{m}$ is used and the interference pattern is observed on a screen kept $1.5\mathrm{m}$  away. The separation between the successive bright fringes on the screen is:

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 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 $=6400\mathrm{k}\mathrm{m}$  )