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A cylinder of radius R made of a material of thermal conductivity K1 is surrounded by a cylindrical shell of inner radius R and other radius 2R made of material of thermal conductivity K2. The 2 ends of combined system are maintained at two different temperatures. There is no loss of heat across the clinical surface and the system is in steady state calculate the effective thermal conductivity of the

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On what factors, does the average kinetic energy of gas molecules

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At very low pressure and high temperature, the real gas behaves like ideal gas.

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Explain why Two bodies at different temperatures `T_1` and `T_2` if brought in thermal contact do not necessarily settle to the mean temperature (`T_1` + `T_2`

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Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure (STP : 1 atmospheric pressure, 0 °C). Show that it is 22.4

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Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion? (a) a = 0.7x (b) a = –200`x^2` (c) a = –10x (d) a =

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Figures correspond to two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anti-clockwise) are indicated on each figure. Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P, in each

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A cylindrical piece of cork of density of base area A and height h floats in a liquid of density `ρ_l`. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period `T=2πsqrt((hρ)/(ρ_lg))` where ρ is the density of cork. (Ignore damping due to viscosity of the

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Two sitar strings A and B playing the note ‘Ga’ are slightly out of tune and produce beats of frequency 6 Hz. The tension in the string A is slightly reduced and the beat frequency is found to reduce to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of

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One end of a long string of linear mass density 8.0 × 10–3 kg m–1 is connected to an electrically driven tuning fork of frequency 256 Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90 kg. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At t = 0, the left end (fork end) of the string x = 0 has zero transverse displacement (y = 0) and is moving along positive y-direction. The amplitude of the wave is 5.0cm. Write

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The density of the atmosphere at sea level is 1.29 kg/`m^3`. Assume that it does not change with altitude. Then how high would the atmosphere

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Two syringes of different cross-sections (without needles) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are 1.0 cm and 3.0 cm respectively. (a) Find the force exerted on the larger piston when a force of 10 N is applied to the smaller piston. (b) If the smaller piston is pushed in through 6.0 cm, how much does the larger piston move

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A metal block of area 0.10 `m^2` is connected to a 0.010 kg mass via a string that passes over an ideal pulley (considered massless and frictionless), as in Fig. . A liquid with a film thickness of 0.30 mm is placed between the block and the table. When released the block moves to the right with a constant speed of 0.085 m `s^(-1)`. Find the coefficient of viscosity of the

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A manometer reads the pressure of a gas in an enclosure as shown in Fig. (a) When a pump removes some of the gas, the manometer reads as in Fig. 10.25 (b) The liquid used in the manometers is mercury and the atmospheric pressure is 76 cm of mercury. (a) Give the absolute and gauge pressure of the gas in the enclosure for cases (a) and (b), in units of cm of mercury. (b) How would the levels change in case (b) if 13.6 cm of water (immiscible with mercury) are poured into the right limb of the manometer

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A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? Mass of the satellite = 200 kg; mass of the earth = 6.0×1024 kg; radius of the earth = `6.4 × 10^6` m; G = `6.67 × 10^(–11)` N `m^2`

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A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s–1. If 20% of its initial energy is lost due to martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it ? Mass of mars = `6.4×10^(23)` kg; radius of mars = 3395 km; G = G = `6.67 × 10^(–11)` N `m^2`

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The oxygen molecule has a mass of `5.30 × 10^(-26)` kg and a moment of inertia of `1.94×10^(-46)` kg `m^2` about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500 m/s and that its kinetic energy of rotation is two thirds of its kinetic energy of translation. Find the average angular velocity of the

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A particle executing S.H.M. has a maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s2 . The period of oscillation

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The displacement time graph of a particle executing S.H.M. is shown in Fig. Which of the following statement is/are

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Show that for a particle executing S.H.M, velocity and displacement have a phase difference of

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