JEE Main 2024 · 4 Apr 2024 Shift 2

Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit.

1. AT² = 4π²r³/(GM)
2. BT² = 4π²r²/(GM)
3. CT² = 4π²r³
4. DT² = 4π²r/(GM²)

A 2 kg brick begins to slide over a surface which is inclined at an angle of 45° with respect to horizontal axis. The co-efficient of static friction between their surfaces is:

1. A1
2. B1/√3
3. C1.7
4. D0.5

A 90 kg body placed at 2R distance from surface of earth experiences gravitational pull of : (R = Radius of earth, g = 10 m s⁻²)

1. A300 N
2. B225 N
3. C120 N
4. D100 N

Correct formula for height of a satellite from earths surface is:

1. A(T²R²/(4π²g))¹ᐟ³ − R
2. B(T²R²g/(4π))¹ᐟ² − R
3. C(T²R²g/(4π²))⁻¹ᐟ³ + R
4. D(T²R²g/(4π²))¹ᐟ³ − R

Given below are two statements : Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube. In the light of the above statements, choose the correct answer from the options given below :

1. ABoth Statement I and Statement II are true.
2. BBoth Statement I and Statement II are false.
3. CStatement I is true but Statement II is false.
4. DStatement I is false but Statement II is true.

A sample of gas at temperature T is adiabatically expanded to double its volume. Adiabatic constant for the gas is γ = 3/2. The work done by the gas in the process is: (μ = 1 mole)

1. ART[2 − √2]
2. BRT[√2 − 2]
3. CRT[2√2 − 1]
4. DRT[1 − 2√2]

The translational degrees of freedom (fₜ) and rotational degrees of freedom (fᵣ) of CH₄ molecule are:

1. Afₜ = 3 and fᵣ = 2
2. Bfₜ = 2 and fᵣ = 3
3. Cfₜ = 3 and fᵣ = 3
4. Dfₜ = 2 and fᵣ = 2

A charge q is placed at the center of one of the surface of a cube. The flux linked with the cube is:

1. Aq/(2ε₀)
2. Bq/(4ε₀)
3. Cq/(8ε₀)
4. DZero