CSS 2022 Physics Combined Papers Past Paper

Paper details

Examination

CSS

Year

2022

Subject

Physics

Paper

Combined Papers

Subject type

Optional

Mode

Subjective

Questions recorded from this paper

These 12 question wordings are transcribed from CSS Vista’s structured Physics past-paper record for CSS 2022.

1. Q3 · Mechanics(a) Assume that a star has uniform density. Show that the gravitational pressure P (08) is proportional to V-3/4 where V is volume. (b) Derive expressions for potential and electric field associated with point (07) charge located near an infinite grounded conducting plane. (c) Determine equation of motion of masses attached to the string of at-wood (05) (20) machine by Lagrangian methods.
2. Q4 · Mechanics(a) Q cm3 of water flows per second through a horizontal tube of uniform bore of (08) radius r & of length L. Another tube of half the length but radius 2r is connected in parallal to same pressure head. What will be the total quantity of water flowing / sec through these two tubes? (b) A linear quadruple is an arrangement of a system of charges which consist of (07) −2 at the origin and + at the two point(± , 0,0). Show that at distances much greater than( . . ≫ ), the potential may be written in the approximate form = ! (3 #$% & − 1), ≫ (c) Two soap bubbles with radii r1 and r2 coalescs to form a bigger bubble of (05) (20) radii r. Show that r = ( r12 +r22 )1/2.
3. Q2 · Waves and Oscillations, Optics(a) A particle of unit mass moves in potential V(x) = ax2 + b/ x2 where a & b are (08) positive constants. Find the angular frequency of small oscillations? (b) A hollow spherical shell carries charge density = in region ≤ ≤ . (07) Find the electric field in three regions (i) < (ii) < < (iii) > . (c) A projectile is fired in such a way that its horizontal range is equal to three times (05) (20) its maximum height. Determine its angle of projection.
4. Q5 · Phase and Group velocity(a) Explain wave function. Derive wave formula and explain phase and group (08) velocity. (b) Two semi-infinite grounded metal plates parallel to each other and to the xz- (07) plane are located at ( = 0 and ( = planes, respectively. The left ends of these two plates at ) = 0, are closed off by a strip of width and extend to infinity in the z-direction. The strip is insulated from both the plates and is maintained at a specific potential ((). Find the potential distribution in the slot. (c) A two level system has energies 0& E. The level with zero energy is non- (05) (20) degenerate while the level with energy E is triply degenerate. Find the mean energy of a classical particle in this system at temperature T.
5. Q8 · Electromagnetic wave equation(a) An ensemble of non-interacting spin -1/2 particles is in contact with a heat (08) bath at temperature T & is subjected to an external magnetic field. Each particle can be in one of the two quantum states of energies ε0. If the mean energy per particle is –ε0/2, then find free energy per particle? (b) Derive the electromagnetic wave equation in vacuum and also describe the (07) properties of monochromatic electromagnetic waves. (c) Discuss adiabatic demagnetization using TDS equations mathematically in (05) (20) detail?
6. Q6 · temperature(a) Explain the particle in finite potential well with all possible cases and (08) solutions and make a comparison with infinite potential well. (b) The potential (&) is specified on the surface of a hollow sphere, of (07) radius *. Find potential inside the sphere. (c) A particle is confined to region x>0 by a potential which increases linearly as (05) (20) u(x) = u0x. Find the mean position of particle at temperature T.
7. Q7 · temperature(a) When a gas expands adiabatically its volume is doubled while its absolute (08) temperature is decreased by a factor 1.32. Compute number of degree of freedom of gas molecule? (b) State and prove Ampere’s Law. (07) (c) Find the rms speed of oxygen molecules at O0c? (05) (20)
8. Q2 · Electric field due to point charges(a) An electric dipole, comprising a positive charge and a negative charge− , is (10) placed on the x-axis. Each charge is at the same distance from the origin. The total separation between the charges is 2 .Calculate the electric field due to these charges along the y-axis at the point P, which is at a distance y from the origin. Assume ≫ ( = 8.85×10 ). (b) Write down a mathematical expression to evaluate electric field at a distance (6) from the source charge in vector form. Sketch the graph of as a function of . (c) Define electric field and a dipole.
9. Q5 · Capacitance(a) Four charged particles of charge q, 2q, 3q and 4p are at the corners of a square (8) of side ‘a’ arranged in counter clockwise direction. Determine (i) the electric field at the location of charge q and (ii) the total electric force exerted on q. (b) A parallel plate capacitor has a plate separation of 1 mm. Calculate the surface (6) area of each plate of the capacitor to obtain a capacitance of 1F. Is it possible to produce such a capacitor in the lab? Comment. ( = 8.85×10 ). (c) Define (6) (20) (i) Capacitance (ii) The unit of capacitance (iii) Surface charge density
10. Q7 · Capacitance(a) Discuss the motion of a charged particle of mass , charge and velocity # in (8) a magnetic field B which is directed into the plane of paper. (b) Discuss atomic description of dielectrics. (6) (c) Let be the separation between the parallel plates of a capacitor of capacitance (6) (20) in the absence of a dielectric material. A slab of a material of dielectric constant $ and thickness %& is placed between the plates. Calculate the capacitance in the presence of the dielectric material.
11. Q4 · Magnetic properties of matter(a) Discuss intrinsic and extrinsic semiconductors. (10) (b) Describe the properties of diamagnetic, paramagnetic and ferromagnetic (6) materials. (c) Briefly discuss the Landé g factor. (4) (20)
12. Q6 · particle in a box(a) Set up the Schrodinger wave equation for a particle of mass confined in a (10) one-dimensional box which has perfectly rigid walls at = 0 and = !. Solve the differential equation to find the expressions for energy and the eigen wave functions of the particle. (b) Sketch the graphs for the first three eigen wave functions " , " and " . (5) (c) Plot the graphs for the probability densities corresponding to " , " and " . (5) (20)

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