(a)What is Gradient of a scalar function? Give its physical significance and show that ∇φ = ∂φ/∂x î + ∂φ/∂y ĵ + ∂φ/∂z k̂ [10]
(b)Define the term 'acceleration' and find its Cartesian components. [6]
(c)If A = xz³î – 2x²zĵ + 2yz⁴k̂, then find curl of A at the point (1,-1,1) [4]
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Q. 3
(a)Explain the rotational kinetic energy and determine its formula for a disc, hoop and sphere. [10]
(b)What do you mean by the term 'inertia' in physics? Calculate respectively the rotational inertia of a solid cylinder and a hollow cylinder about an axis of symmetry. [6]
(c)Calculate the angular speed of the second's hand, minutes hand and hour's hand of a watch. [4]
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Q. 4
(a)What was Physics like before relativity and how did Einstein come up with his theory? Mathematically explain how mass and energy is interchangeable? [10]
(b)Discuss in detail the relativity of length using Einstein's special theory of relativity. [6]
(c)Calculate the mass equivalent of energy from an antenna radiating 10KW for 24 hours. [4]
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Q. 5
(a)Define capillarity and derive an expression for the rise of liquid in a capillary tube to show that the height of the liquid column supported is inversely proportional to the radius of the tube. [10]
(b)What are fluids? Write their important characteristics. [6]
(c)A cylindrical swimming pool has radius 2m and depth 1.3m. It is filled completely with salt water. Given, density of salt water = 1.03x10 3 kgm -3 , volume of water = 16.34m 3 , and the atmospheric pressure = 1.013x10 5 Pa. Calculate the pressure at the bottom of the pool. [4]
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Q. 6
(a)For a wave travelling through a medium, demonstrate that the total energy per unit volume is always equal to one half the kinetic and one half the potential energy. [10]
(b)The longitudinal waves can pass through solids. How it is possible and on what parameters the velocity of such waves will depend? [6]
(c)The angular Vibrational frequency of CO molecule is 0.6x10 15 s -1 . Calculate the amount of work required for stretching it by 0.5Å from the equilibrium position. [4]
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Q. 7
(a)An ideal gas is enclosed in a cylinder with movable piston. Calculate the work done on such gas and show that pressure force is non-conservative. [10]
(b)State and briefly explain the intermolecular forces. [6]
(c)Oxygen gas having a volume of 1130cm³ at 42°C and a pressure of 101kPa expanded until its volume is 1530cm³ and its pressure is 106kPa. Find the number of moles of oxygen in the system and its final temperature. [4]
The 2023 CSS Physics paper set by the Federal Public Service Commission. Question wording only; questions marked “Not yet checked” have not been compared with the official paper yet. Open the official paper beside the questions to check any of them.
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