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Part II
Q. 2
(a)The Vectors A ⃗ = 2 i ^ + j ^ + 3 k ^ , B ⃗ = i ^ − 2 j ^ − 2 k ^ \vec{A} = 2\hat{i} + \hat{j} + 3\hat{k}, \vec{B} = \hat{i} - 2\hat{j} - 2\hat{k} A = 2 i ^ + j ^ + 3 k ^ , B = i ^ − 2 j ^ − 2 k ^ . Find the magnitudes of A & B, A.B and Projection of B on A.
(b)Prove that A ⃗ × ( B ⃗ × C ⃗ ) = B ⃗ ( A ⃗ ⋅ C ⃗ ) − C ⃗ ( A ⃗ ⋅ B ⃗ ) \vec{A} \times (\vec{B} \times \vec{C}) = \vec{B}(\vec{A} \cdot \vec{C}) - \vec{C}(\vec{A} \cdot \vec{B}) A × ( B × C ) = B ( A ⋅ C ) − C ( A ⋅ B ) . [6]
(c)Are the units vectors in the cylindrical and spherical coordinate system constant vectors? Explain. [4]
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Q. 3
(a)State Kepler's laws of planetary motion and prove Law of Areas Law of periods.
(b)Use Maxwell's equations to derive the electromagnetic wave equation. [10]
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Q. 4
(a)What is Doppler's effect?
(b)A stationary observer detects sound of frequency 250 hertz emitted from a source at rest. He detects sound of frequency 750 hertz when source is moving towards him with constant velocity. Determine velocity of sound. (Velocity of sound = 341 m/Sec.) [6]
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Q. 5
(a)Describe the Young's double slit experiment and find the conditions of constructive and destructive interference.
(b)The double slit arrangement is illuminated by light of wavelength 546nm, the slits are 0.12mm apart and the screen on which the interference pattern appears is 55cm away.
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(10)
Q. 6
(a)Describe the Postulates of relativity.
(b)What is the total energy E of a 2.53 Mev electron? When an energy is used as an adjective, it refers to the Kinetic energy of the particle, here K= 2.53 Mev. [8]
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Q. 7
(a)Derive the expressions of position and time coordinates in frame S' relative to S (Lorentz Transformation). [12]
(b)Derive the Bernoulli's equation of a steady flow. [8]
The 2013 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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