PHYSICS (Properties Of Matter And Mechanics)

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) Define Poisson’s ratio and give limiting values of Poisson’s ratio. If Y, K and s represents

Young’s modulus, Bulk modulus and Poisson’s ratio, then, show that, Y = 3K(1–2σ). [5M]

(B) (i) Obtain an expression for time period of torsional pendulum. [3M]

(ii) A wire of length 1m and diameter 1 mm is damped at one end. Calculate the torque

required to twist other end by 90º. If modulus of rigidity of material of wire is 2.8 × 10^{10}N/m^{2}. [2M]

**OR**

(C) Derive an expression for work done in stretching a wire. [2½M]

(D) Show that for a homogeneous isotropic medium, Y = 2η(1 + σ), where constants have their usual

meaning. [2½M]

(E) Derive an expression for the bending of a beam supported at two ends and loaded in the middle. [2½M]

(F) A beam of square cross section 1cm2 and 1m long is clamped horizontally at one end. When the

load of 1kg is applied to the free end, the depression of the free end is 4 × 10^{–2}m. Calculate

Young’s modulus of the material of the cantiliver. (g = 9.8m/s^{2}) [2½M]

**EITHER**

2. (A) State and prove the Stoke’s law by method of dimensions. Deduce an expression for terminal

velocity of a spherical body, through a viscous medium. [5M]

(B) (i) State and prove Bernoulli’s Theorem. [3M]

(ii) Calculate the mass of water per second initially flowing out of the hole. If the depth of water

in an open tank is 2.5m and a small hole of cross-section 3cm^{2} is made at the bottom of

tank. (ρ= 1000 kg/m^{3}) [2M]

**OR**

(C) What is the effect of temperature on coefficient of viscosity ? Explain. [2½M]

(D) State Newton’s law of viscous force. Obtain an expression for coefficient of viscosity. State its

unit. [2½M]

(E) Distinguish between streamline and turbulent flow. [2½M]

(F) Calculate the mass of water flowing in 10 minutes through a tube 0.1 cm in diameter and 40cm

long under a constant pressure head of 20cm of water. The coefficient of viscosity of water at

room temperature is 8.2 × 10^{–3} poise. [2½M]

**EITHER**

3. (A) Define surface tension. State its units and dimensions. Derive an expression for the height of liquid

column in a capillary tube of radius ‘r’. [5M]

(B) (i) Define Coriolis force. Discuss the applications of the Coriolis force. [3M]

(ii) Find the polar coordinates corresponding to the following Cartesian coordinates :

(a) (1, 0)

(b) (1, 1) [2M]

**OR**

(C) Distinguish between inertial and non-inertial frame of reference with example. [2½M]

(D) State Newton’s law’s of motion. Derive an expression for Newton’s third law from the second law. [2½M]

(E) What is surface energy ? Show that the surface tension of a liquid is equal to its surface energy

per unit area. [2½M]

(F) Calculate the height to which a liquid will rise in a capillary tube of radius 0.2 mm when surface

tension of liquid is 20 × 10^{–3} N/m and density 800 kg/m^{3}. (assuming angle of contact 0º) [2½M]

**EITHER**

4. (A) What is elastic and inelastic collision ? Derive the equations for final velocities of two particles

when the collision between them is perfectly one dimensional elastic. [5M]

(B) (i) Deduce an expression for the moment of inertia of solid cylinder about an axis passing

through its centre and perpendicular to its length. [3M]

(ii) Mass of earth is 6 × 10^{24} kg and its radius is 6400 km. Find the moment of Inertia of earth

about its axis of rotation. [2M]

**OR**

(C) State and prove the law of conservation of energy. [2½M]

(D) Explain the need of multistage rocket to launch the satellite. [2½M]

(E) Explain the term moment of inertia and give its physical significance. [2½M]

(F) Calculate the radius of gyration of solid sphere rotating about its diameter if its radius is 5.0 cm. [2½M]

5. Attempt any ten questions : 1×10=10M

(i) Define angle of twist

(ii) Define compressibility.

(iii) Calculate the bulk modulus of brass. (Y = 10 × 10^{10}N/m^{2} and h = 3.7 × 10^{10}N/m^{2})

(iv) What is Critical Velocity ?

(v) What is Reynold’s number ?

(vi) The critical velocity of fluid flows in capillary tube of radius 0.02 mm is 4 cm/s, what will be the

critical velocity of the same fluid in capillary of radius 0.01 mm ?

(vii) State any two applications of Newton’s laws of motion.

(viii) Mention conditions for the validity of the Stoke’s law.

(ix) Calculate the work done in blowing a soap bubble of radius 10cm and surface tension 30 dyne/cm.

(x) Define centre of mass.

(xi) What do you mean by radius of gyration ?

(xii) The position vectors of two particles of masses 1kg and 3kg at any instant are $Latex \left(2\widehat i+5\widehat j+13\widehat k\right)$m and $Latex \left(-6\widehat i+4\widehat j-2\widehat k\right)$m respectively. Calculate the position vector of centre of

mass at that instant.

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