On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius $$R$$ and making a circular contact of radius $$r$$ with the bottom $$R$$ and making a circular contact of radius $$r$$ with the bottom of the vessel. If $$r<<R$$ and the surface tension of water is $$T,$$ value of $$r$$ just before bubbles detach is: (density of water is $${\rho }_w$$)

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $$d_1$$ and $$d_2$$ are filled in the tube. Each liquid subtends $$90^{\circ }$$ angle at center. Radius joining their interface makes an angle $$\alpha$$ with vertical. Radio {{{d_1}} \over {{d_2}}} is :

The pressure that has to be applied to the ends of a steel wire of length $$10$$ $$cm$$ to keep its length constant when its temperature is raised by $$100^{\circ }C$$ is: (For steel Young's modulus is $$2\times 10^{11}N{m}^{-2}$$ and coefficient of thermal expansion is $$1.1\times 10^{-5}{K}^{-1}$$ )

An open glass tube is immersed in mercury in such a way that a length of $$8$$ $$cm$$ extends above the mercury level. The open end of the tube is then closed and scaled and the tube is raised vertically up by additional $$46$$ $$cm$$. What will be length of the air column above mercury in the tube now? (Atmospheric pressure $$=76$$ $$cm$$ of $$Hg$$)

The current voltage relation of diode is given by $$\mathrm{I}=\left(e^{100V/T}-1\right)mA,$$ where the applied voltage $$V$$ is in volts and the temperature $$T$$ is in degree kelvin. If a student makes an error measuring $$\pm 0.01V$$ while measuring the current of $$5$$ $$mA$$ at $$300$$ $$K,$$ what will be the error in the value of current on $$mA$$?

The forward biased diode connection is:

A particle moves with simple harmonic motion in a straight line. In first $$\tau s,$$ after starting from rest it travels a distance $$a,$$ and in next $$\tau s$$ it travels $$2a,$$ in same direction, then:

During the propagation of electromagnetic waves in a medium :

Match List - $$1$$ (Electromagnetic wave type ) with List - $$2$$ (Its association/application) and select the correct option from the choices given below the lists:

If microwaves, X rays, infracted, gamma rays, ultra-violet, radio waves and visible parts of the electromagnetic spectrum by M, X, I, G, U, R and V, the following is the arrangement in ascending order of wavelength :

A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly :

Match the List - I (Phenomenon associated with electromagnetic radiation) with List - II (Part of electromagnetic spectrum) and select the correct code from the choices given the lists : .tg {border-collapse:collapse;border-spacing:0;} .tg td{font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;} .tg th{font-family:Arial, sans-serif;font-size:14px;font-weight:normal;padding:10px 5px;border-style:solid;border-width:1px;overflow:hidden;word-break:normal;border-color:black;} .tg .tg-13k7{font-size:20px;text-align:left} .tg .tg-p7ly{font-weight:bold;font-size:20px;text-align:center} .tg .tg-fbrz{font-weight:bold;font-size:20px;text-align:center;vertical-align:top} .tg .tg-60hs{font-size:20px;text-align:left;vertical-align:top} List - I List - II (I) Doublet of sodium (A) Visible radiation (II) Wavelength corresponding to temperature associated with the isotropic radiation filling all space (B) Microwave (III Wavelength emitted by atomic hydrogen in interstellar space (C) Short radiowave (IV) Wavelength of radiation arising from two close energy levels in hydrogen (D) X - rays

An electromagnetic wave of frequency 1 $$\times$$ 1014 hertz is propagating along z - axis. The amplitude of electric field is 4 V/m. If $$\in$$0 = 8.8 $$\times$$ 10$$-$$12 C2/N-m2, then average energy density of electric field will be :

Match List I (Wavelength range of electromagnetic spectrum) with List II. (Method of production of these waves) and select the correct option from the options given below the lists.

When a rubber-band is stretched by a distance $$x$$, it exerts restoring force of magnitude $$F=ax+b{x}^2$$ where $$a$$ and $$b$$ are constants. The work done in stretching the unstretched rubber-band by $$L$$ is :

In the circuit shown here, the point $${}^{\prime }{C}^{\prime }$$ is kept connected to point $${}^{\prime }{A}^{\prime }$$ till the current flowing through the circuit becomes constant. Afterward, suddenly, point $${}^{\prime }{C}^{\prime }$$ is disconnected from point $${}^{\prime }{A}^{\prime }$$ and connected to point $${}^{\prime }{B}^{\prime }$$ at time $$t=0.$$ Ratio of the voltage across resistance and the inductor at $$t=L/R$$ will be equal to :

The radiation corresponding to $$3\to 2$$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field $$3\times 10^{-4}T.$$ If the radius of the larger circular path followed by these electrons is $$10.0$$ $$mm$$, the work function of the metal is close to:

Hydrogen $$\left({}_1{H}^1\right)$$, Deuterium $$\left({}_1{H}^2\right)$$, singly ionised Helium $${\left({}_{2}H{e}^4\right)}^{+}$$ and doubly ionised lithium $${\left({}_{3}L{i}^6\right)}^{++}$$ all have one electron around the nucleus. Consider an electron transition from $$n=2$$ to $$n=1.$$ If the wavelengths of emitted radiation are $${\lambda }_1,{\lambda }_2,{\lambda }_3$$ and $${\lambda }_4$$ respectively then approximately which one of the following is correct?

One mole of a diatomic ideal gas undergoes a cyclic process $$ABC$$ as shown in figure. The process $$BC$$ is adiabatic. The temperatures at $$A,B$$ and $$C$$ are $$400$$ $$K$$, $$800$$ $$K$$ and $$600$$ $$K$$ respectively. Choose the correct statement :

Three rods of Copper, Brass and Steel are welded together to form a $$Y$$ shaped structure. Area of cross - section of each rod $$=4c{m}^2.$$ End of copper rod is maintained at $$100^{\circ }C$$ where as ends of brass and steel are kept at $$0^{\circ }C$$. Lengths of the copper, brass and steel rods are $$46,$$ $$13$$ and $$12$$ $$cms$$ respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are $$0.92,0.26$$ and $$0.12$$ $$CGS$$ units respectively. Rate of heat flow through copper rod is: