Physics

An iron rod of volume ${10}^{-3}{\mathrm{m}}^3$ ${}^{}{}^{}$ and relative permeability 1000 is placed as core in a solenoid with 10 turns/cm. If a current of $0.5\mathrm{A}$ $$ is passed through the solenoid, then the magnetic moment of the rod will be:

In adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be $n$ $$ times the initial pressure. The value of $n$ $$ is:

In the circuit shown, charge on the $5\mu \mathrm{F}$ $$ capacitor is:

Two different wires having lengths $L_1$ ${}_{}$ and ${}_{}$ $L_2$ , and respective temperature coefficient of linear 4expansion ${\alpha }_1$ ${}_{}$ and ${\alpha }_2$ ${}_{}$ , are joined end-to-end. Then the effective temperature coefficient of linear expansion is:

Two coherent sources of sound, $S_1$ ${}_{}$ and $S_2$ ${}_{}$ produce source waves of the same wavelength, $\lambda =1\mathrm{m}$ $$ , in phase. $S_1$ ${}_{}$ and ${\mathrm{S}}_2$ ${}_{}$ are placed $1.5\mathrm{m}$ $$ apart (see fig). A listener located at $\mathrm{L}$ $$ , directly in front of $S_2$ ${}_{}$ finds that the intensity is at a minimum when he is $2\mathrm{m}$ $$ away from ${\mathrm{S}}_2$ ${}_{}$ . The listener moves away from $S_1$ ${}_{}$ , keeping his distance from $S_2$ ${}_{}$ fixed. The adjacent maximum of intensity is observed when the listener is at a distance $d$ $$ from ${}_{}$ $S_1$ . Then, $d$ $$ is:

A hollow spherical shell at outer radius $\mathrm{R}$ floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is $\frac{27}{8}$ w.r.t water, the value of r is.

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is $$ $30\mathrm{c}\mathrm{m}$ and the refractive index of the lens material is 1.5 , then the focal length of the lens (in $\mathrm{c}\mathrm{m}$ $$ ) is(Ray Optics)

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is $300\mathrm{m}/\mathrm{s}$ $$ , the frequency difference between the fundamental and second harmonic of this pipe is $\mathrm{H}\mathrm{z}$ $$

A body $A$ $$ , of mass $m=0.1\mathrm{k}\mathrm{g}$ $$ has an initial velocity of $3\hat{i}{\mathrm{m}\mathrm{s}}^{-1}$ $\stackrel{}{}{}^{}$ . It collides elastically with another body, $B$ $$ of the same mass which has an initial velocity of $5\hat{j}{\mathrm{m}\mathrm{s}}^{-1}$ $\stackrel{}{}{}^{}$ . After collision, A moves with a velocity $\stackrel{?}{v}=4(\hat{i}+\hat{j})$ $\stackrel{}{}\stackrel{}{}\stackrel{}{}$ . The energy of $$ $B$ after collision is written as $\frac{}{}$ $\frac{x}{10}\mathrm{J}$ . The value of $x$ $$ is