Not yet checked 6 of 7 questions have not yet been compared with the official paper.
Part II
Q. 2
(a)What is the curl of a vector field? Explain its physical significance. [10]
(b)What is vector triple product? Show that A ⃗ × ( B ⃗ × C ⃗ ) = ( A ⃗ ⋅ C ⃗ ) B ⃗ − ( A ⃗ ⋅ B ⃗ ) C ⃗ \vec{A} \times (\vec{B} \times \vec{C}) = (\vec{A} \cdot \vec{C})\vec{B} - (\vec{A} \cdot \vec{B})\vec{C} A × ( B × C ) = ( A ⋅ C ) B − ( A ⋅ B ) C [6]
(c)If ϕ=2x2y2z4 then find the div grad ϕ . [4]
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Q. 3
(a)State and explain Kepler's law of areas. [8]
(b)A spaceship of mass m = 4.50 4.50×103 kg is in a circular Earth orbit of radius r = 8.00 8.00×106 m and period T0 = 118.6 min = 7.119 7.119×103 s when a thruster is fired in the forward direction to decrease the speed to 96.0% of the original speed. What is the period T of the resulting elliptical orbit? [6]
(c)Which has greater magnitude, the angular momentum of the Earth (relative to its center) associated with its rotation on its axis or the angular momentum of the Earth (relative to the center of its orbit) associated with its orbital motion around the Sun? [6]
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Q. 4
(a)Explain the equivalence of mass and energy. [6]
(b)Explain two tests of time dilation i.e microscopic and macroscopic clocks. [8]
(c)The mean lifetime of stationary muons is measured to be 2.2000 ms. The mean lifetime of high-speed muons in a burst of cosmic rays observed from Earth is measured to be 16.000 ms. To five significant figures, what is the speed parameter β of these cosmic-rays muons relative to Earth? [6]
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Q. 5
(a)What is viscosity? Explain in detail. What is the effect of temperature on viscosity? [8]
(b)Caster oil, which has a density of 0.96 0.96×103 kg/m³ at room temperature, is forced through a pipe of circular cross section by a pump that maintains a gauge pressure of 950 Pa. The pipe has a diameter of 2.6 cm and a length of 65 cm. The castor oil emerging from the free end of the pipe at atmospheric pressure is collected. After 90 s, a total of 1.23 kg has been collected. What is the coefficient of viscosity of the castor oil at this temperature? [5]
(c)A liquid flows through a horizontal pipe whose inner radius is 2.52 cm. The pipe bends upward through a height of 11.5 m where it widens and joins another horizontal pipe of inner radius 6.14 cm. What must the volume flux be if the pressure in the two horizontal pipes is the same? [7]
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Q. 6
(a)What is damped harmonic oscillator? Write its equation of motion and find its solution. [10]
(b)The amplitude of a lightly damped oscillator decreases by 3.0% during each cycle. [4]
(c)What percentage of the mechanical energy of the oscillator is lost in each cycle? [6]
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Q. 7
(a)What are travelling waves? Find the rate at which energy is transported by a wave travelling along a string. [5]
(b)A string has linear density μ = 525 g/m and is under tension T = 45 N. We send a sinusoidal wave with frequency f = 120 Hz and amplitude ym = 8.5 mm along the string. At what average rate does the wave transport energy? [5]
(c)Two sinusoidal waves with the identical wavelengths and amplitudes travel in opposite directions along a string with a speed of 10 cm/s. If the time interval between instants when the string is flat is 0.50 s, what is the wavelength of the waves? [10]
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Q. 8
(a)Explain the volume and pressure corrections in ideal gas law as suggested by van der Waals. [10]
(b)For oxygen the van der Waals coefficients have been measured to be a = 0.138 J ⋅ m 3 / m o l 2 a = 0.138 \ J \cdot m^3/mol^2 a = 0.138 J ⋅ m 3 / m o l 2 and b = 3.18 b=3.18×10−5m3/mol . Assume that 1.00 mol of oxygen at T = 50 K is confined to a box of volume 0.0224 m³. What pressure does the gas exert according to (a) the ideal gas law and (b) the van der Waals equation? [5]
(c)State and explain the zeroth law of thermodynamics. [5]
The 2020 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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