JEE Main 2023 · 13 Apr 2023 Shift 2

In the equation [X + a/Y²][Y − b] = RT, X is pressure, Y is volume, R is universal gas constant and T is temperature. The physical quantity equivalent to the ratio a/b is:

1. AEnergy
2. BPressure gradient
3. CImpulse
4. DCoefficient of viscosity

The distance travelled by an object in time t is given by s = (2.5)t². The instantaneous speed of the object at t = 5 s will be:

1. A5 ms⁻¹
2. B12.5 ms⁻¹
3. C25 ms⁻¹
4. D62.5 ms⁻¹

A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then length of train B is:

1. A80 m
2. B120 m
3. C200 m
4. D320 m

A vehicle of mass 200 kg is moving along a levelled curved road of radius 70 m with angular velocity of 0.2 rad/s. The centripetal force acting on the vehicle is:

1. A14 N
2. B2240 N
3. C560 N
4. D2800 N

Given below are two statements: Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases. Statement II : Escape velocity is independent of the radius of the planet. In the light of above statements, choose the most appropriate answer form the options given below

1. ABoth Statement I and Statement II are correct
2. BBoth Statement I and Statement II are incorrect
3. CStatement I is correct but statement II is incorrect
4. DStatement I is incorrect but statement II is correct

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : A spherical body of radius (5 ± 0.1) mm having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is 4%. Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius. In the light of the above statements, choose the correct answer from the options given below

1. ABoth A and R are true and R is the correct explanation of A
2. BBoth A and R are true but R is NOT the correct explanation of A
3. CA is true but R is false
4. DA is false but R is true

Two planets A and B of radii R and 1.5 R have densities ρ and ρ/2 respectively. The ratio of acceleration due to gravity at the surface of B to A is:

1. A2:1
2. B2:3
3. C3:4
4. D4:3

The initial pressure and volume of an ideal gas are P₀ and V₀. The final pressure of the gas when the gas is suddenly compressed to volume V₀/4 will be : (Given γ = ratio of specific heats at constant pressure and at constant volume)

1. AP₀
2. B4P₀
3. CP₀(4)ᵞ
4. DP₀(4)¹ᐟᵞ