201962 marks18 questions
9 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) 2019, Paper 1, Physics, published by JEE (Advanced). The official PDF
Consider a spherical gaseous cloud of mass density ρ(r) in free space where r is the radial distance from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the common center with the same kinetic energy K. The force acting on the particles is their mutual gravitational force. If ρ(r) is constant in time, the particle number density n(r) = ρ(r)/m is [G is universal gravitational constant]
A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is V₀. A hole with a small area α4πR² (α ≪ 1) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?
A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changes with time (t) as T(t) = T₀(1 + βt¹⁄⁴), where β is a constant with appropriate dimension while T₀ is a constant with dimension of temperature. The heat capacity of the metal is,
In a radioactive sample, ⁴⁰₁₉K nuclei either decay into stable ⁴⁰₂₀Ca nuclei with decay constant 4.5 × 10⁻¹⁰ per year or into stable ⁴⁰₁₈Ar nuclei with decay constant 0.5 × 10⁻¹⁰ per year. Given that in this sample all the stable ⁴⁰₂₀Ca and ⁴⁰₁₈Ar nuclei are produced by the ⁴⁰₁₉K nuclei only. In time t × 10⁹ years, if the ratio of the sum of stable ⁴⁰₂₀Ca and ⁴⁰₁₈Ar nuclei to the radioactive ⁴⁰₁₉K nuclei is 99, the value of t will be, [Given: ln 10 = 2.3]
A charged shell of radius R carries a total charge Q. Given Φ as the flux of electric field through a closed cylindrical surface of height h, radius r and with its center same as that of the shell. Here, center of the cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces. Which of the following option(s) is/are correct? [ε₀ is the permittivity of free space]
Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement(s) is/are correct?
Two identical moving coil galvanometers have 10 Ω resistance and full scale deflection at 2 μA current. One of them is converted into a voltmeter of 100 mV full scale reading and the other into an Ammeter of 1mA full scale current using appropriate resistors. These are then used to measure the voltage and current in the Ohm’s law experiment with R = 1000 Ω resistor by using an ideal cell. Which of the following statement(s) is/are correct?
A parallel plate capacitor of capacitance C has spacing d between two plates having area A. The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness δ = d/N. The dielectric constant of the mᵗʰ layer is Kₘ = K (1 + m/N). For a very large N (> 10³), the capacitance C is α (Kε₀A/(d ln 2)). The value of α will be ________. [ε₀ is the permittivity of free space]
A liquid at 30°C is poured very slowly into a Calorimeter that is at temperature of 110°C. The boiling temperature of the liquid is 80°C. It is found that the first 5 gm of the liquid completely evaporates. After pouring another 80 gm of the liquid the equilibrium temperature is found to be 50°C. The ratio of the Latent heat of the liquid to its specific heat will be ______°C. [Neglect the heat exchange with surrounding]