JEE Main 2024 · 9 Apr 2024 Shift 1

The dimensional formula of latent heat is:

1. A[ML²T⁻²]
2. B[M⁰L²T⁻²]
3. C[MLT⁻²]
4. D[M⁰LT⁻²]

A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals with speeds 9 m/s and 15 m/s respectively. The average speed of the particle during the motion is:

1. A10 m/s
2. B8 m/s
3. C8.8 m/s
4. D9.2 m/s

A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle θ with the horizontal. The weight experienced by the person is:

1. AW cos θ
2. BW sin θ
3. CW
4. DW/2

A light unstretchable string passing over a smooth light pulley connects two blocks of masses m₁ and m₂. If the acceleration of the system is g/8, then the ratio of the masses m₂/m₁ is:

1. A8 : 1
2. B9 : 7
3. C4 : 3
4. D5 : 3

A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation v = α√x, where α is a constant. The total work done by all the forces applied on the particle during its displacement from x = 0 to x = d, will be:

1. Amd/(2α²)
2. Bmα²d/2
3. Cm/(2α²d)
4. D2mα²d

An astronaut takes a ball of mass m from earth to space. He throws the ball into a circular orbit about earth at an altitude of 318.5 km. From earth’s surface to the orbit, the change in total mechanical energy of the ball is xG Mₑm/(21Rₑ). The value of x is (take Rₑ = 6370 km):

1. A9
2. B10
3. C11
4. D12

A sphere of relative density σ and diameter D has concentric cavity of diameter d. The ratio of D/d, if it just floats on water in a tank is:

1. A((σ − 1)/σ)^(1/3)
2. B(σ/(σ − 1))^(1/3)
3. C((σ − 2)/(σ + 2))^(1/3)
4. D((σ + 1)/(σ − 1))^(1/3)

A sample of 1 mole gas at temperature T is adiabatically expanded to double its volume. If adiabatic constant for the gas is γ = 3/2, then the work done by the gas in the process is :

1. ART [2 − √2]
2. BRT [2 + √2]
3. CR/T [2 − √2]
4. DT/R [2 + √2]