JEE Advanced 2023 · Paper 2

Young’s modulus of elasticity Y is expressed in terms of three derived quantities, namely, the gravitational constant G, Planck’s constant h and the speed of light c, as Y = cᵅhᵝGᵞ. Which of the following is the correct option?

1. Aα = 7, β = −1, γ = −2
2. Bα = −7, β = −1, γ = −2
3. Cα = 7, β = −1, γ = 2
4. Dα = −7, β = 1, γ = −2

A particle of mass m is moving in the xy-plane such that its velocity at a point (x, y) is given as v⃗ = α(yx̂ + 2xŷ), where α is a non-zero constant. What is the force F⃗ acting on the particle?

1. AF⃗ = 2mα²(xx̂ + yŷ)
2. BF⃗ = mα²(yx̂ + 2xŷ)
3. CF⃗ = 2mα²(yx̂ + xŷ)
4. DF⃗ = mα²(xx̂ + 2yŷ)

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is n. The internal energy of one mole of the gas is Uₙ and the speed of sound in the gas is vₙ. At a fixed temperature and pressure, which of the following is the correct option?

1. Av₃ < v₆ and U₃ > U₆
2. Bv₅ > v₃ and U₃ > U₅
3. Cv₅ > v₇ and U₅ < U₇
4. Dv₆ < v₇ and U₆ < U₇