202066 marks18 questions
8 of its 18 questions are here. The rest have a figure or are still being checked, so for now they're only in the official PDF.
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Source: JEE (Advanced) 2020, Paper 2, Physics, published by JEE (Advanced). The official PDF
A train with cross-sectional area Sₜ is moving with speed vₜ inside a long tunnel of cross-sectional area S₀ (S₀ = 4Sₜ). Assume that almost all the air (density ρ) in front of the train flows back between its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be p₀. If the pressure in the region between the sides of the train and the tunnel walls is p, then p₀ − p = 7/(2N) ρvₜ². The value of N is ________.
A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total mass is 480 kg. Its effective volume giving the balloon its buoyancy is V. The balloon is floating at an equilibrium height of 100 m. When N number of sandbags are thrown out, the balloon rises to a new equilibrium height close to 150 m with its volume V remaining unchanged. If the variation of the density of air with height h from the ground is ρ(h) = ρ₀e⁻ʰ⁄ʰ⁰, where ρ₀ = 1.25 kg m⁻³ and h₀ = 6000 m, the value of N is _________.
In an X-ray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance d from the cathode. The target is kept at a potential V higher than the cathode resulting in emission of continuous and characteristic X-rays. If the filament current I is decreased to I/2, the potential difference V is increased to 2V, and the separation distance d is reduced to d/2, then
Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is α. The spheres are now immersed in a dielectric liquid of density 800 kg m⁻³ and dielectric constant 21. If the angle between the strings remains the same after the immersion, then
A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be p₀. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R − a). For a ≪ R the magnitude of the work done in the process is given by (4πp₀Ra²)X, where X is a constant and γ = Cₚ/Cᵥ = 41/30. The value of X is________.
Two capacitors with capacitance values C₁ = 2000 ± 10 pF and C₂ = 3000 ± 15 pF are connected in series. The voltage applied across this combination is V = 5.00 ± 0.02 V. The percentage error in the calculation of the energy stored in this combination of capacitors is _______.
A cubical solid aluminium (bulk modulus = −V dP/dV = 70 GPa) block has an edge length of 1 m on the surface of the earth. It is kept on the floor of a 5 km deep ocean. Taking the average density of water and the acceleration due to gravity to be 10³ kg m⁻³ and 10 ms⁻², respectively, the change in the edge length of the block in mm is _____.
A container with 1 kg of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is 700 Wm⁻² and it is absorbed by the water over an effective area of 0.05 m². Assuming that the heat loss from the water to the surroundings is governed by Newton’s law of cooling, the difference (in ℃) in the temperature of water and the surroundings after a long time will be _____________. (Ignore effect of the container, and take constant for Newton’s law of cooling = 0.001 s⁻¹, Heat capacity of water = 4200 J kg⁻¹ K⁻¹)