PHYSICS (Oscillations, Kinetic Theory Of Gases And Thermodynamics)

Optional Paper—1

Time : 3 Hours

Maximum Marks : 50

N.B. :— (1) All questions are compulsory and carry equal marks.

(2) Draw well labelled diagram wherever necessary.

**EITHER**

1. (A) What is damped harmonic oscillator ? Derive the differential equation for it and obtain an

equation for its displacement. [5M]

(B) (i) Show that for damped harmonic oscillator total energy decreases exponentially with time. [3M]

(ii) A mass of 0.25 kg is suspended from the lower end of a vertical spring having force

constant 25N/m. The mechanical resistance of the system is 1.5N S/m. The mass is displaced

vertically and released. Find whether the motion is oscillatory. [2M]

**OR**

(C) Obtain an expression for power dissipated in damped harmonic oscillators. [2½M]

(D) Define simple harmonic motion. Obtain general differential equation of simple harmonic motion. [2½M]

(E) Show that the resultant of two SHMs at right angles to each other having equal periods and

amplitudes but phase difference 90º is a circle. [2½M]

(F) A particle execute simple harmonic motion with time period of 5 sec. and amplitude 5 cm.

Calculate the maximum velocity of particle. [2½M]

**EITHER**

2. (A) Derive the differential equation of forced harmonic oscillator. Solve the differential equation to

obtain steady state solution. [5M]

(B) (i) What is amplitude resonance ? Explain the effect of damping on it. [3M]

(ii) If the resonant frequencies of acoustic system is 280 Hz and half requencies are 200 Hz

and 360 Hz respectively, calculate quality factor. [2M]

**OR**

(C) What is quality factor ? Give the physical significance of quality factor of forced oscillator. [2½M]

(D) Show that Resonance absorption bandwidth $Latex \left(P_2-P_1\right)=\frac Rm$ [2½M]

(E) What is piezoelectric effect ? Discuss one of its application. [2½M]

(F) A damped oscillator of mass 2 × 10^{–3} kg and force constant 500N/m is subjected to a periodic

force of variable frequency. Find the frequency of force for the velocity resonance. If the mechanical

resistance 2 × 10^{–3} Ns/m, calculate quality factor for the oscillator. [2½M]

**EITHER**

3. (A) What are the transport phenomena in gases ? Derive an expression for coefficient of diffusion of

a gas. [5M]

(B) (i) State and prove law of equipartition of energy. [3M]

(ii) Calculate the diameter of a molecule, if n = 2.79 × 10^{19} molecule per c.c. and mean free

path l = 2.2 × 10^{–6}cm. [2M]

**OR**

(C) Define mean free path. Discuss the effect of temperature and pressure on mean free path. [2½M]

(D) Derive the expression for coefficient of viscosity of gas on the basis of transport phenomenon of gas. [2½M]

(E) Derive the equation for van der Waal’s constant a and b. [2½M]

(F) Calculate critical pressure of gas having van der Waal’s constant a = 0.58 Nm^{4}/kg mole^{2} and

b = 0.0316 m^{3}/mole. [2½M]

**EITHER**

4. (A) What is Joule-Thomson effect ? Derive the expression for Joule-Thomson co-efficient. [5M]

(B) (i) Define entropy. Show that change in entrophy in reversible cycle is zero. [3M]

(ii) Calculate the change in entropy when 1kg of water is raised from 0ºC to 100ºC, Sp. heat

capacity of water is 1 kcal/kg k. (1 kcal = 4184 J). [2M]

**OR**

(C) Write down the difference between reversible process and irreversible process. [2½M]

(D) State first law of thermodynamics. Give the importance and limitations of it. [2½M]

(E) Show that in irreversible process, entropy always increases. [2½M]

(F) A Carnot engine working in a cycle absorb 100 kcal. If the temperature of source and sink are

327ºC and 27ºC, calculate the heat rejected to the sink. [2½M]

5. Attempt any TEN questions : 1×10M

(i) What is Liassajous Figure ?

(ii) Define free oscillation.

(iii) A mass of 1kg is attached to a spring of force constant 16N/m. Find its natural frequency.

(iv) What is velocity resonance ?

(v) Define mechanical impedance.

(vi) Show that the unit of damping coefficient ‘b’ is sec^{–1}.

(vii) State Boyle’s law.

(viii) Define self diffusion.

(ix) Define critical temperature and critical pressure.

(x) Write down the expression for Clausius-Claperon equation.

(xi) What is cyclic process ?

(xii) State third law of thermodynamics.

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