**2013**

**(November)**

**PHYSICS**

**(General)**

**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

- Under what condition, angular momentum of a rotating body will be equal to its moment of inertia?

- K = 1
- M = 1
- = 1

- True.
- False.

- The total energy of a simple pendulum during experiment in our laboratories is always constant.

- True.
- False.
- In ideal case only.

- Stress and strain are

- Directly proportional according to Young’s law.
- Inversely proportional according to Hooke’s law.
- Directly proportional according to Hooke’s law.

- If be the rise of river water and seawater in a capillary tube, then

- The cylinder of a Carnot’s engine consists of

- Conducting wall and non-conducting base.
- Non-conducting wall and conducting base.
- Conducting wall and conducting base.

- Which of the following is correct?

- The Carnot’s heat engine is perfectly reversible.
- The efficiency is independent of the working substance.
- Both of the above are correct.

- Rayleigh-Jeans law agrees well with the experimental result

- At law frequencies.
- At high frequencies.
- None of the above.

2. Answer any eight of the following questions: 3x8=24

- 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

- 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
- 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
- Show that the value of Poisson’s ratio of an elastic material varies from – 1 to 0.5. 3
- Name and derive the principle 3
- 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
- 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
- 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
- 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

- Find an expression for moment of inertia of a spherical shell about a diameter. Express its radius of gyration. 4+1=5
- 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?

- Derive the following equation of motion for a simple pendulum having length and mass of the bob by using Lagrange’s equations: 5

- Why and which of iron and rubber is more elastic? Derive an expression relating Y, n and K. 5
- 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
- What is entropy? Show that in a reversible process the change in entropy can be expressed as. 2+3=5
- 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
- Write a brief essay on ultraviolet catastrophe. 5
- 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

- Radius of gyration.
- Hamiltonian.
- Second law of thermodynamics.
- Kirchhoff’s law.