Physics

The radius of gyration of a uniform rod of length $$ $\mathcal{l}$ , about an axis passing through a point $\frac{\mathcal{l}}{4}$ $\frac{}{}$ away from the centre of the rod, an perpendicular to it 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)

The current $I_1$ ${}_{}$ (in A) flowing through $$ $1\mathrm{\Omega }$ resistor in the following circuit is

At time $\mathrm{t}=0$ $$ magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next $5\mathrm{s}$ $$ , then induced EMF in the loops is:

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

A parallel plate capacitor has plates of area A separated by distance ' $d$ $$ ' between them. It is filled with a dielectric which has a dielectric constant that varies as $k\left(n\right)=k(1+$ $\alpha n)$ $$ $$ where ' $$ $x$ ' is he distance measured from one of the plates.

If $\left(\alpha \mathrm{d}\right)<<1$ $$ , the total capacitance of the system is best given by the expression:

The plot that depicts the behavior of the mean free time $\tau$ $$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature $\left(T\right)$ $$ , qualitatively, is: (Graphs are schematic and not drawn to scale)

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

Visible light of wavelength $6000*{10}^{-8}\mathrm{c}\mathrm{m}$ ${}^{}$ falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at ${60}^{?}$ ${}^{}$ from the central maximum. If the first minimum is produced at ${\theta }_1$ ${}_{}$ then ${\theta }_1$ ${}_{}$ 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