JEE Main 2024 · 6 Apr 2024 Shift 1

Four particles A, B, C, D of mass m/2, m, 2m, 4m, have same momentum, respectively. The particle with maximum kinetic energy is :

1. AA
2. BB
3. CC
4. DD

A light string passing over a smooth light pulley connects two blocks of masses m₁ and m₂ (where m₂ > m₁). If the acceleration of the system is g/√2, then the ratio of the masses m₁/m₂ is:

1. A(√2 − 1)/(√2 + 1)
2. B(√3 + 1)/(√2 − 1)
3. C(1 + √5)/(√2 − 1)
4. D(1 + √5)/(√5 − 1)

To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is Rₑ, g = acceleration due to gravity on the surface of earth):

1. A2mgRₑ
2. B4mgRₑ
3. C½mgRₑ
4. DmgRₑ

A train starting from rest first accelerates uniformly up to a speed of 80 km/h for time t, then it moves with a constant speed for time 3t. The average speed of the train for this duration of journey will be (in km/h) :

1. A70
2. B30
3. C40
4. D80

A small ball of mass m and density ρ is dropped in a viscous liquid of density ρ₀. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

1. Amg(1 − ρ₀/ρ)
2. Bmg(ρ₀/ρ − 1)
3. Cmg(1 − ρρ₀)
4. Dmg(1 + ρ/ρ₀)

The specific heat at constant pressure of a real gas obeying PV² = RT equation is:

1. ACᵥ + R/(2V)
2. BCᵥ + R
3. CR
4. DR/3 + Cᵥ

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :

1. A2√2/1
2. B1/(2√2)
3. C1/32
4. D1/4

σ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is :

1. Aσ/ε₀
2. Bσ/2ε₀
3. Cσ/(ε₀R)
4. Dσ/4ε₀