JEE Advanced 2025 · Paper 1

A person sitting inside an elevator performs a weighing experiment with an object of mass 50 kg. Suppose that the variation of the height y (in m) of the elevator, from the ground, with time t (in s) is given by y = 8[1 + sin(2πt/T)], where T = 40π s. Taking acceleration due to gravity, g = 10 m/s², the maximum variation of the object’s weight (in N) as observed in the experiment is ____

A cube of unit volume contains 35 × 10⁷ photons of frequency 10¹⁵ Hz. If the energy of all the photons is viewed as the average energy being contained in the electromagnetic waves within the same volume, then the amplitude of the magnetic field is α × 10⁻⁹ T. Taking permeability of free space μ₀ = 4π × 10⁻⁷ Tm/A, Planck’s constant h = 6 × 10⁻³⁴ Js and π = 22/7, the value of α is____

A single slit diffraction experiment is performed to determine the slit width using the equation, bd = Dmλ, where b is the slit width, D the shortest distance between the slit and the screen, d the distance between the mth diffraction maximum and the central maximum, and λ is the wavelength. D and d are measured with scales of least count of 1 cm and 1 mm, respectively. The values of λ and m are known precisely to be 600 nm and 3, respectively. The absolute error (in μm) in the value of b estimated using the diffraction maximum that occurs for m = 3 with d = 5 mm and D = 1 m is ___

Consider an electron in the n = 3 orbit of a hydrogen-like atom with atomic number Z. At absolute temperature T, a neutron having thermal energy kB T has the same de Broglie wavelength as that of this electron. If this temperature is given by T = Z²h²/(απ²a₀²mN kB), (where h is the Planck’s constant, kB is the Boltzmann constant, mN is the mass of the neutron and a₀ is the first Bohr radius of hydrogen atom) then the value of α is ___