HCS Mains Frontier IAS: Physics Optional Paper 2014

HCS Mains Physics Optional Paper 2014

Time : 3 Hours                                                                                                                        M.M.: 150
                                
Note: Attempt five questions. All questions carry equal marks. Question number 1 is compulsory. Answer any two questions from part I and two questions from part II. The Parts of the same questions must be answered together and must not be interposed between answers to other questions. 
In case of any discrepancy in the English and Hindi versions. The English version will be taken as final.

l. Attempt any four of the following:                                                                    (4x7.5=30)

(a) Write down and explain Bernoulli's equation. Using this equation discuss the principle of the lift of an airplane.

(b) Describe the principle of equipartition of energy in Thermodynamics. Using this principle, discuss about the specific heat of diatomic molecules.

(c) Write a short note on the principle of holography.

(d) Find out the value of current flowing through and the potential difference across each resistance and also E1in the following circuit. Assume internal resistance of the two cells to be negligible.

(e) Give a classification of the following fundamental particles: photons, π⁺, Ρ, e¯, n, v_e, μ¯, Σ⁺. Also state which of these are stable and which ones have finite lifetime.

f) Identify the following Gate. Give its truth table and explain the same.

                                                                       Part-I

2. (a) A man whose mass is 90 kg is in a lift ( elevator). Determine the force the floor of the lift exerts on him when ( i ) the lift goes up with a uniform speed, (ii) the lift accelerate up to 3 ms-2 and (iii), the cable of the lift brakes and the lift falls freely.                       (3+3+4=10)

(b) Consider two frames of reference S' and S and assume S' to be moving with respect to S along x-axis with a velocity v. Using Lorentz Transformation for position coordinates and time, obtain expression for velocity of a body as measured in S' in terms of that measured in S.   (10)                                                                                                                   

c) Consider two observers O and O' such that frame of reference attached to O'is rotating with an angular velocity ω with respect to the frame attached to O. Obtain appropriate expressions for acceleration of a particles as observed by O in terms of that by O' .  (10)
                                                                                                                                
3. (a) What is a Carnot cycle? Deduce an expression for efficiency of a Cannot engine working between Source temperature T₁ and Sink temperature T₂.   (10)

(b) Make a qualitative sketch of Maxwellian distribution of velocities of gas molecules at two temperatures T1, and T2, (assume T1, > T2,). Deduce expression for root mean square velocity and calculate the same for H2 gas (given k : 1.38 X 10^-23 J/K and mH= 1.674X10^-27kg).    (4+3+3=10)                                                                                                             

c) Using Debye model, obtain an expression for specific heat (at constant volume) of solids for temperatures much below Debye temperature.     (10)

4. (a) Assume a particle of mass m subjected to an elastic force and a velocity dependent damping force. Let this be applied upon by a force F= F_° cos(ωt). Set up the equation of motion for the particle (solution is not required). Write down the expression for velocity amplitude of the oscillator (no derivation is required). At which frequency of the applied force does the energy resonance occur ?     (3+3+2=8)

(b) Two transverse of simple harmonic waves A and B (of same frequency) of amplitudes 5 units and 2 units superpose with phase difference (i) π/2 and (ii)π. Obtain ratio of the intensities of the superposed patterns.  (8)                                                              

c) A diffraction grating of width 2 cm and having 20,000 lines is used in the third order in range of wavelength 5500Å. What is the smallest frequency interval (in cm-1 units) that the grating can resolve?  (8)                                                                                                      

(d) State two special characteristics of the LASER source in relation to an ordinary light source. Briefly explain how they are achieved in a LASER source.    (2+4)  

                                                                Part - II

5. (a) Consider two parallel plates with equal but opposite charges. Using Gauss's law obtain the electric field in the region between the two plates.  (10)

(b) Consider a current carrying thin rectilinear wire of infinite length. Obtain an expression for magnitude of the magnetic field at a normal distance R from the wire.     (10)

c) A capacitor of 0.001 µF is connected in parallel with a 2 mH coil of resistance 0.5Ω Calculate (i) the frequency at which the current from an AC source to this circuit is minimum and (ii) selectivity of the circuit.   (5+5)                                                              

6. (a) Describe Raman effect. Explain the same on the basis of quantized nature of energy states.    (2+8)                                                                                                          

(b) Solve Schrodinger equation for the particle in one dimensional potential well of width 'a' and infinite depth and obtain expression for the energy values of the particle. Make a schematic sketch of the wave functions for first three energy states in the potential well. (6+4)

(c) consider the nuclear reaction
            ₀n¹+₉₂U^{235 →}₄₂Mo⁹⁸+₅₄Kr¹³⁶+₂₀n¹                                                       (10)

Calculate the energy released (in eV) in the fission of one 92U235nucleus fmasses (in amu) of ₀n¹, ₉₂U²³⁵, ₄₂Mo⁹⁸ and ₅₄Kr¹³⁶ are 1.0087, 235.0439, 97.9054 and 135.9170 respectively. 

7 a). Discuss the forward and reverse bias condition of a p -n junction diode and draw the characteristic curve Explain cutin (or threshold) voltage of the diode.      (6+4)

(b) Giving a suitable circuit diagram, explain the working of a common emitter transistor amplifier. Comment on the features of its voltage and current gain and input and output impedances.    (6+4)                                                                                                          

(c) Explain the working of a bridge rectifier circuit.    (10)