# Physics CSS Paper I 2022

FEDERAL PUBLIC SERVICE COMMISSION

COMPETITIVE EXAMINATION – 2022

FOR RECRUITMENT TO POST IN BS – 17

UNDER THE FEDERAL GOVERNMENT

PHYSICS, PAPER I

TIME ALLOWED: THREE HOURS

PART – I (MCQs): MAXIMUM 30 MINUTES

PART – I (MCQs): MAXIMUM MARKS = 20

PART – II MAXIMUM MARKS = 80

NOTE:

(i) Part – II is to be attempted on the separate Answer Book.

(ii) Attempt ONLY FOUR questions from PART – II. ALL questions carry EQUAL marks.

(iii) All the parts (if any) of each Question must be attempted at one place instead of at different places.

(iv) Candidate must write Q. No. in the Answer Book in Accordance with Q. No. in the Q. Paper.

(v) No Page / Space be left blank between the answers. All the blank pages of Answer Book must be crossed.

(iv) Extra attempt of any question or any part of the attempted question will not be considered.

PART II

Q 2 (a) A particle of unit mass moves in potential V(x) = ax^{2} + b/ x^{2} where a & b are positive constants. Find the angular frequency of small oscillations? (8)

(b) A hollow spherical shell carries charge density p = k/r^{2} in region a ≤ r ≤ b. Find the electric field in three regions (i) r < b (ii) a < r < b (iii) r > b. (07)

(c) A projectile is fired in such a way that its horizontal range is equal to three times its maximum height. Determine its angle of projection. (05) (20)

Q 3 (a) Assume that a star has uniform density. Show that the gravitational pressure P is proportional to V-3/4 where V is volume. (08)

(b) Derive expressions for potential and electric field associated with point charge q located near an infinite grounded conducting plane. (07)

(c) Determine equation of motion of masses attached to the string of at-wood machine by Lagrangian methods. (05) (20)

Q 4 (a) Q cm^{3} of water flows per second through a horizontal tube of uniform bore of radius r & of length L. Another tube of half the length but radius 2r is connected in parallel to same pressure head. What will be the total quantity of water flowing / sec through these two tubes? (08)

(b) A linear quadruple is an arrangement of a system of charges which consist of —2Q at the origin and +Q at the two point (±d, 0,0). Show that at distances much greater than (i.e. r >> d), the potential may be written in the approximate form (07)

V = Qd^{2}/(4πε_{0} r^{3})(3cos(θ)-1),r^{2}≫d^{2}

V = Qd^{2}/4Pi x (3cos^{2}-1), r^{2} >>d^{2}

(c) Two soap bubbles with radii r1 and r2 coalesces to form a bigger bubble of radii r. Show that r = (r1^{2} +r2^{2} )1/2. (05) (20)

Q 5 (a) Explain wave function. Derive wave formula and explain phase and group velocity. (08)

(b) Two semi-infinite grounded metal plates parallel to each other and to the xz- plane are located at y = 0 and y = a planes, respectively. The left ends of these two plates at x = 0, are closed off by a strip of width a and extend to infinity in the z-direction. The strip is insulated from both the plates and is maintained at a specific potential V_{0}(y). Find the potential distribution in the slot. (07)

(c) A two level system has energies O& E. The level with zero energy is non- degenerate while the level with energy E is triply degenerate. Find the mean energy of a classical particle in this system at temperature T. (05) (20)

Q 6 (a) Explain the particle in finite potential well with all possible cases and solutions and make a comparison with infinite potential well. (08)

(b) The potential V_{0}(θ) is specified on the surface of a hollow sphere, of radius R. Find potential inside the sphere. (07)

(c) A particle is confined to region x>0 by a potential which increases linearly as u(x) = u_{o}x. Find the mean position of particle at temperature T. (05) (20)

Q 7 (a) When a gas expands adiabatically its volume is doubled while its absolute temperature is decreased by a factor 1.32. Compute number of degree of freedom of gas molecule? (08)

(b) State and prove Ampere’s Law. (07)

(c) Find the rms speed of oxygen molecules at O^{0}c? (05) (20)

Q 8 (a) An ensemble of non-interacting spin -1/2 particles is in contact with a heat bath at temperature T & is subjected to an external magnetic field. Each particle can be in one of the two quantum states of energies εO. If the mean energy per particle is -ε0/2, then find free energy per particle? (08)

(b) Derive the electromagnetic wave equation in vacuum and also describe the properties of monochromatic electromagnetic waves. (07)

(c) Discuss adiabatic demagnetization using TDS equations mathematically in detail? (05) (20)