JEE Main 2024 · 30 Jan 2024 Shift 1

A particle of mass m is projected with a velocity ‘u’ making an angle of 30° with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is:

1. A(√3/2)(mu²/g)
2. Bzero
3. C(√3/16)(mu³/g)
4. Dmu³/(√2 g)

A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m. The impulse of force imparted by the ground to the body is given by: (given, g = 9.8 m/s²)

1. A2.39 kg ms⁻¹
2. B43.2 kg ms⁻¹
3. C23.9 kg ms⁻¹
4. D4.32 kg ms⁻¹

The gravitational potential at a point above the surface of earth is −5.12 × 10⁷ J/kg and the acceleration due to gravity at that point is 6.4 m/s². Assume that the mean radius of earth to be 6400 km. The height of this point above the earth’s surface is:

1. A1600 km
2. B1000 km
3. C540 km
4. D1200 km

Young’s modules of material of a wire of length ‘L’ and cross-sectional area A is Y. If the length of the wire is doubled and cross-sectional area is halved then Young’s modules will be :

1. A4 Y
2. BY/4
3. CY
4. D2Y

At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47 °C ?

1. A20 K
2. B80 K
3. C−73 K
4. D4 K

The electrostatic potential due to an electric dipole at a distance ‘r’ varies as :

1. A1/r
2. B1/r²
3. C1/r³
4. Dr

An electric toaster has resistance of 60 Ω at room temperature (27 °C). The toaster is connected to a 220 V supply. If the current flowing through it reaches 2.75 A, the temperature attained by toaster is around : (if α = 2 × 10⁻⁴/°C)

1. A694 °C
2. B1667 °C
3. C1694 °C
4. D1235 °C

A series L.R circuit connected with an ac source E = (25 sin 1000 t) V has a power factor of 1/√2. If the source of emf is changed to E = (20 sin 2000 t) V, the new power factor of the circuit will be :

1. A1/√2
2. B1/√3
3. C1/√5
4. D1/√7