Not yet checked 6 of 7 questions have not yet been compared with the official paper.
Part II
Q. 2
(a)A particle of unit mass moves in potential V ( x ) = V(x)=ax2+b/x2 where a & b are positive constants. Find the angular frequency of small oscillations? [8]
(b)A hollow spherical shell carries charge density ρ=k/r2 in region a a≤r≤b . Find the electric field in three regions (i) r < a r < a r < a (ii) a < r < b a < r < b a < r < b (iii) r > b r > b r > b . [7]
(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. [5]
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(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. [8]
(b)Derive expressions for potential and electric field associated with point charge q located near an infinite grounded conducting plane. [7]
(c)Determine equation of motion of masses attached to the string of at-wood machine by Lagrangian methods. [5]
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(20)
Q. 4
(a)Q cm³ 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 2 r 2r 2 r is connected in parallel to same pressure head. What will be the total quantity of water flowing / sec through these two tubes? [8]
(b)A linear quadruple is an arrangement of a system of charges which consist of −2Q at the origin and + Q +Q + Q at the two points (±d,0,0) . Show that at distances much greater than (i.e. r ≫ d r \gg d r ≫ d ), the potential may be written in the approximate form V = Q d 2 4 π ϵ 0 r 3 ( 3 cos 2 θ − 1 ) , r 2 ≫ d 2 V = \frac{Qd^2}{4 \pi \epsilon_0 r^3} (3 \cos^2 \theta - 1), r^2 \gg d^2 V = 4 π ϵ 0 r 3 Q d 2 ( 3 cos 2 θ − 1 ) , r 2 ≫ d 2 [7]
(c)Two soap bubbles with radii r1 and r2 coalesces to form a bigger bubble of radii r . Show that r = r 1 2 + r 2 2 r = \sqrt{r_1^2 + r_2^2} r = r 1 2 + r 2 2 . [5]
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Q. 5
(a)Explain wave function. Derive wave formula and explain phase and group velocity. [8]
(b)Two semi-infinite grounded metal plates parallel to each other and to the xz-plane are located at y = 0 y = 0 y = 0 and y = a y = a y = a planes, respectively. The left ends of these two plates at x = 0 x = 0 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 V0(y) . Find the potential distribution in the slot. [7]
(c)A two level system has energies 0 0 0 & 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 . [5]
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(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. [8]
(b)The potential V0(θ) is specified on the surface of a hollow sphere, of radius R . Find potential inside the sphere. [7]
(c)A particle is confined to region x>0 by a potential which increases linearly as u ( x ) = u(x)=u0x . Find the mean position of particle at temperature T . [5]
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(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? [8]
(b)State and prove Ampere's Law. [7]
(c)Find the rms speed of oxygen molecules at Oºc? [5]
(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 ϵ0 . If the mean energy per particle is –ϵ0/2 , then find free energy per particle? [8]
(b)Derive the electromagnetic wave equation in vacuum and also describe the properties of monochromatic electromagnetic waves. [7]
(c)Discuss adiabatic demagnetization using TDS equations mathematically in detail? [5]
The 2022 CSS Physics paper set by the FPSC. Question wording only; questions marked “Not yet checked” have not been compared with the official paper yet.
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