Dibrugarh University Question Papers: Mechanics and Thermodynamics' 2013

Course: 101
(Mechanics and Thermodynamics)
Full Marks: 80
Pass Marks: 32
Time: 3 hours
The figures in the margin indicate full marks for the questions

1. Choose the correct answer from the following questions: 1x8=8
  1. Under what condition, angular momentum of a rotating body will be equal to its moment of inertia?
  1. K = 1
  2. M = 1
  3. = 1
  1. Angular momentum is not related to linear momentum.
  1. True.
  2. False.
  1. The total energy of a simple pendulum during experiment in our laboratories is always constant.
  1. True.
  2. False.
  3. In ideal case only.
  1. Stress and strain are
  1. Directly proportional according to Young’s law.
  2. Inversely proportional according to Hooke’s law.
  3. Directly proportional according to Hooke’s law.
  1. If be the rise of river water and seawater in a capillary tube, then
  1. The cylinder of a Carnot’s engine consists of
  1. Conducting wall and non-conducting base.
  2. Non-conducting wall and conducting base.
  3. Conducting wall and conducting base.
  1. Which of the following is correct?
  1. The Carnot’s heat engine is perfectly reversible.
  2. The efficiency is independent of the working substance.
  3. Both of the above are correct.
  1. Rayleigh-Jeans law agrees well with the experimental result
  1. At law frequencies.
  2. At high frequencies.
  3. None of the above.
2. Answer any eight of the following questions: 3x8=24
  1. An object rotating about an axis has the following physical quantities:
Rotational kinetic energy = E
Angular velocity =
Moment of inertia = I
Angular momentum = J
Establish the relation 3
  1. The moment of inertia of a sphere about a diameter is. Calculate moment of inertia of the sphere about a tangent and hence show that its radius of gyration is. 3
  2. The excess pressure inside a soap bubble is equal to the pressure of mercury column of height 20 cm. Find the radius of the bubble. Given density of Hg is 0.8 g/cm3 and surface tension of soap solution is. 3
  3. Show that the value of Poisson’s ratio of an elastic material varies from – 1 to 0.5. 3
  4. Name and derive the principle 3
  5. Define adiabatic and isothermal changes. Express the variation of pressure with volume of a gas in both types of changes mathematically. 1+1+1/2+1/2=3
  6. State zeroth law in thermodynamics. Explain the law by drawing a neat diagram and use the word ‘adiabatic’ in the explanation, if necessary. 1+1+1/2+1/2=3
  7. What do you mean by a black-body radiation? Draw the black-body radiation graph between emission of energy with frequency and point out the portion obeying Rayleigh-Jeans law and the portion obeying Wien’s law. Write the basic mathematical idea forwarded by Planck in order to explain the black-body radiation successfully. 1+(1/2 x 3)+1/2=3
  8. Define cohesive force and adhesive force. Explain what balances the further rise of liquid in a capillary tube. 1/2+1/2+2=3
3. Answer any eight of the following questions: 5x8=40
  1. Find an expression for moment of inertia of a spherical shell about a diameter. Express its radius of gyration. 4+1=5
  2. Correct the expression of a body rolling down an inclined plane
where the symbols have their usual meanings. Show that the accelerations of a disc and a sphere of same radius are and respectively. Which body will reach the bottom first?
  1. Derive the following equation of motion for a simple pendulum having length and mass of the bob by using Lagrange’s equations: 5
  1. Why and which of iron and rubber is more elastic? Derive an expression relating Y, n and K. 5
  2. Which of mercury and water surfaces the pressure just below the surface is less? Calculate the work done in blowing a soap bubble from a radius 0.1 m to 0.2 m, if the surface tension of soap solution is 1+4=5
  3. What is entropy? Show that in a reversible process the change in entropy can be expressed as. 2+3=5
  4. Calculate the change in entropy when (i) 5kg of water at 100 is converted into steam at the same temperature (L = 540 cal/g) and (ii) 10 g of ice at 0 is converted into water at the same temperature (L = 80 cal/g). In which case the change in entropy is more? 5
  5. Write a brief essay on ultraviolet catastrophe. 5
  6. Calculate the moment of inertia of a uniform plane rectangular lamina about an axis passing through its centre and parallel to its breadth. 5
4. Write short notes on any two of the following: 4x2=8
  1. Radius of gyration.
  2. Hamiltonian.
  3. Second law of thermodynamics.
  4. Kirchhoff’s law.