HPSC Mains 2003: Optional Subject Physics Frontier IAS

HCS Mains 2003 Optional Paper: Physics

HPSC Mains 2003: In this post, we will discuss the HCS mains 2003 optional Physics paper.

Time: 3 hours                                                                                                                                Marks:150

Note: Attempt any Five questions. All questions carry equal marks. Q. No. 1 is compulsory. Answer two questions from Part I and two Questions from Part II. The parts of the same question must be answered together and must not be interposed between answers to other questions.

1. Write critical notes on any four of the following: 4×7.5=30 marks
(a) Elastic and Inelastic Collisions
(b) Joul-Kelvin Effect
(c) Fourier Theorem
(d) Quality Factor of a circuit (Q-factor)
(e) Cyclotron
(f) Logic Gates

Part-I

2. (a) State the fundamental postulates of special theory of relativity and deduce the Lorentz Transformations. 12 marks

(b) Write Bernouli’s theorem for the flow of an ideal liquid. Use it to prove that the velocity of efflux of a liquid emerging from a hole in the wall of a vessel is √(2gh), where h is the height of the liquid level above the hole. 12 marks

(c) Prove that the centre of mass of two particles subject to their mutual interaction alone (central force) moves with a constant velocity. 6 marks

3. (a) State and explain Maxwell’s law of distribution of velocities. Briefly explain ‘conduction’, mean free path’ and ‘viscosity’ on the basis of kinetic theory. 12 marks

(b) Summarize the characteristics of black body radiation. Derive Plank’s law of black body radiations and obtain Stefan’s fourth power law from it. 12 marks

(c) The luminosity of a star is 20,000 times that of the sun. If the surface temperature of the sun is 6000°K, find the surface temperature of the star? 6 marks

4. (a) Solve the differential equation of a damped harmonic oscillator. Investigate the conditions under which the oscillations are said to be under damped overdamped and critically damped. 12 marks

(b) Explain the process of stimulated emission. Draw a neat diagram to represent the component of ‘Ruby Laser’. Briefly explain the operation. 12 marks

(c) A diffraction grating which has 4000 lines to a cm is used at normal incidence. Calculate the dispersive power of the grating in the third-order spectrum in the wavelength region 5000Å. 6 marks

Part-II

5. (a) Define Faraday’s law of electromagnetic induction. Express Faraday’s law in Integral and differential forms. Obtain an expression for induced e.m.i. 12 marks

(b) State and prove Gauss’s law in electrostatics. Obtain an expression for the electric field due to a charged cylindrical conductor. 12 marks

(c) A 50 Hz A.C. circuit has a 10 mH inductor and a 2-ohm resistor in series. What is the power factor? 6 marks

6. (a) Write down Schrodinger equation for a particle in a box. Solve it to obtain eigen Functions and show that the eigen values are discrete. 12 marks

(b) Describe briefly different mechanisms through which -rays are absorbed in matter. 12 marks

(c) Compute the value of Plank’s constant h if photo-electron ejected from the surface of certain metal by light of frequency 2.2×10¹⁵Hz are fully retarded by a reverse potential of 6.6V and those ejected by light of frequency 4.6×10¹⁵Hz are stopped by a reverse potential of 16.5V. 6 marks

7. (a) Find the hole and electron concentrations in a p-type semiconductor, if the acceptor density is 10²⁰ atoms/m3 and the intrinsic concentration is 2.5×10¹⁹per m³ at 300°K. 12 marks

(b) A full-wave P-N diode rectifier use load resistor of 1500 ohms. No filter is used. Assume each diode to have idealized characteristics with R_f=10 ohms and R_r=∞. Since wave voltage applied to each diode has amplitude of 30 volts and frequency 50 Hz. Calculate Peak current, dc load current and rms load current. 12 marks

(c) What is an Oscillator? Explain the essentials of a transistor oscillator. 6 marks