Not yet checked 4 of 7 questions have not yet been compared with the official paper.
Part II
Q. 2
(a)Define gradient. Find the gradient of the magnitude of a position vector r. What conclusion do you derive from your result? [4]
(b)Sketch a function V = -yx^ + xy^. Find curl V. What would be its divergence? [6]
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(10)
Q. 3
(a)What is theory of relativity? Consider two inertial frames, A and B, with axes parallel and origins O,O' coinciding at t = t' = 0 and B moving with uniform velocity v along x-axis of A. Letting γ = 1 / 1 − ( v 2 / c 2 ) \gamma = 1/\sqrt{1-(v^2/c^2)} γ = 1/ 1 − ( v 2 / c 2 ) , the Lorenz transformation A \rightarrow B is x ′ = γ ( x − v t ) , y ′ = y , z ′ = z , t ′ = γ ( t − v x / c 2 ) x' = \gamma(x − vt), y' = y, z' = z, t'= \gamma(t − vx/c²) x ′ = γ ( x − v t ) , y ′ = y , z ′ = z , t ′ = γ ( t − v x / c 2 ) . From the principle of equivalence of inertial frames infer the inverse Lorenz transformation B \rightarrow A. [8]
(b)We can write one of Maxwell's equation of B in inertial frame 1 as B B⋅dl1=μ0(ϵ0∂ϕe1/∂t1=i1) . Write it in inertial frame 2 according to Einstein's principle of relativity. Does B1=B2 ? [4]
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(12)
Q. 4
(a)State and prove Bernoulli's Theorem. [12]
(b)If the speed of flow past the lower surface of an airplane wing is 110 m/s. What speed of flow over the upper surface will give a pressure difference of 900 Pa between upper and lower surface? Take the density of air to be 1.3 1.3×10−3 g/cm3 . [8]
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(20)
Q. 5
(a)Describe waves and its types. Derive an expression for speed of wave on a stretched string by Newton's second law. [8]
(b)The equation of a transverse wave on a string is Y = ( 2 mm ) sin [ ( 20 m − 1 ) x – ( 600 s − 1 ) t ] Y = (2 \text{mm}) \sin [(20 \text{m}^{-1})x – (600 \text{s}^{-1})t] Y = ( 2 mm ) sin [( 20 m − 1 ) x – ( 600 s − 1 ) t ] . The tension in the string is 15N. What is the wave speed? Find the linear density of this string in grams/meter. [4]
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(12)
Q. 6
(a)What is interference of waves? Describe all the necessary conditions for constructive and destructive interference. Explain one interferometer. [6]
(b)Two sound waves from two coherent sources with same frequency 450 Hz are traveling in the same direction at 330 m/s. What is the phase difference of the waves at a point that is 4.4m from one source and 4m from the other source. [8]
(14)
Q. 7
(a)State and explain Second Law of Thermodynamics. Prove that Clausius and Kelvin-Plank statements of it are equivalent. [6]
(b)A Carnot engine operates between the temperatures 850 K and 300 K. The engine performs 1200 J of work each cycle, which takes 0.25 s. Calculate its efficiency and its average power. What are the rates of heat input and heat exhaust per cycle? [8]
The 2009 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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