# HPSC Mains 2003: Optional Subject Physics Frontier IAS

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**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 2.2×10^{15}Hz are fully retarded by a reverse potential of 6.6V and those ejected by light of frequency 4.6×10^{15}Hz 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 10^{20} atoms/m3 and the intrinsic concentration is 2.5×10^{19}per m^{3 }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**