Physics (Optional)

Q1. Answer any four of the following:

() A particle is subjected to two rectangular S.H.M.s given by x = a sin(ωt + φ) and (a) y = b sin(ωt). Show that for a = b and φ = π/2 the resultant path of the particle is circle.

() (b) What is a chromatic aberration? Represent it diagrammatically. Describe with a diagram, working of Ramsden's eyepiece.

() (c) Describe stroboscopic method to determine the frequency of a tuning fork. Hence determine the frequency of A.C. Define packing fraction and show that packing fraction for BCC crystal structure.

() (d) Explain intensity level of a sound. Give its formula.

() (e) Calculate the change in intensity level when the intensity of sound increases 10 times its original intensity.

• (b) What is a chromatic aberration? Represent it diagrammatically. Describe with a diagram, working of Ramsden's eyepiece.
• (c) Describe stroboscopic method to determine the frequency of a tuning fork. Hence determine the frequency of A.C. Define packing fraction and show that packing fraction for BCC crystal structure.
• (d) Explain intensity level of a sound. Give its formula.

Q2. Derive an expression for M.I. of solid sphere about its diameter and about its tangent.

() (a) Tangent.

() (b) Assuming that the earth is a homogeneous sphere of radius 6.4 × 10³ km and density 5.4 gm/cm^3, calculate the moment of inertia about its axis of rotation and rotational K.E. of the earth when spinning about its axis.

• (a) Tangent.
• (b) Assuming that the earth is a homogeneous sphere of radius 6.4 × 10³ km and density 5.4 gm/cm^3, calculate the moment of inertia about its axis of rotation and rotational K.E. of the earth when spinning about its axis.

Q3. Define surface tension in terms of surface energy. Give its S.I. unit and C.G.S. unit. Explain angle of contact. Obtain the relation between surface tension, excess pressure and radius of curvature of thin film. Hence find out the excess pressure for a liquid drop in a liquid, spherical soap bubble and spherical drop of liquid.

() (a)

() (b) With the help of schematic diagram, explain the working of Otto engine. Explain Otto cycle with an indicator diagram. Hence deduce the expression for efficiency of Otto engine.

Q4. What is interference of light? Obtain condition for constructive and destructive interference in the reflected system of rays from parallel thin film.

() (a)

() (b) State and explain Coulomb's law in electrostatics. Express it in vector form. Derive an expression for the electric potential at any point due to an electric dipole. Hence deduce the electric potential due to dipole at an axial point and at an equatorial point.

() (c) Obtain an expression for the current flowing through the circuit containing inductance, resistance and capacitance connected in series with an emf e = e0 sin ωt. Hence explain the phenomenon of resonance in series L-C-R circuit.

Q5. Distinguish between Fresnel and Fraunhofer class of diffraction.

() (a)
(i) State Brewster's law of polarization.
(ii) Obtain relation between three electric vectors i.e. D = ε0 E + P.

() (b)
(i) State Ohm's law in electricity. Using Ohm's law derive the relation j = σ E.