Practice Questions

Q7. A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil = 0.8, specific gravity of ice = 0.9) JEE Main 2024 (08 Apr Shift 2) JEE Main Previous Year Paper (1) 1 : 1 (2) 5 : 4 (3) 8 : 9 (4) 9 : 10

Q7. A sphere of relative density σ and diameter D has concentric cavity of diameter d. The ratio of Dd , if it just floats on water in a tank is : (1) ( σ+2σ−2 ) 1/3 (2) ( σ−1σ )1/3 (3) σ−1 1/3 (4) σ+1 1/3 ( σ ) ( σ−1 )

Q7. 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) 2mgRE (2) 4mgRE (3) mgRE (4) 1/2mgRE

Q7. A small spherical ball of radius 𝑟, falling through a viscous medium of negligible density has terminal velocity 𝑣. Another ball of the same mass but of radius 2𝑟, falling through the same viscous medium will have terminal velocity: (1) 𝑣 (2) 𝑣 2 4 (3) 4𝑣 (4) 2𝑣

Q7.Match List-I with List-II : List-I List-II (A) A force that restores an elastic body of unit area to its original state (I) Bulk modulus (B) Two equal and opposite forces parallel to opposite faces (II) Young's modulus Forces perpendicular everywhere to the surface per unit area (C) (III) Stress same everywhere (D) Two equal and opposite forces perpendicular to opposite faces (IV) Shear modulus Choose the correct answer from the options given below : (1) (A)-(IV), (B)-(II), (C)-(III), (D)-(I) (2) (A)-(III), (B)-(IV), (C)-(I), (D)-(II) (3) (A)-(II), (B)-(IV), (C)-(I), (D)-(III) (4) (A)-(III), (B)-(I), (C)-(II), (D)-(IV)

Q7. A wire of length L and radius r is clamped at one end. If its other end is pulled by a force F , its length increases by l. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become: (1) 3 times (2) 32 times (3) 4 times (4) 2 times

Q7. An artillery piece of mass 𝑀1 fires a shell of mass 𝑀2 horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is : 𝑀1 𝑀2 (1) (2) ( 𝑀1 + 𝑀2 ) 𝑀1 (3) 𝑀2 (4) 𝑀1 ( 𝑀1 + 𝑀2 ) 𝑀2

Q7. Given below are two statements: Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water. Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water. In the light of the above statements, choose the most appropriate from the options given below (1) Both Statement I and Statement II are true (2) Both Statement I and Statement II are false (3) Statement I is true but Statement II is false (4) Statement I is false but Statement II is true

Q7. A real gas within a closed chamber at 27∘C undergoes the cyclic process as shown in figure. The gas obeys PV 3 = RT equation for the path A to B. The net work done in the complete cycle is (assuming R = 8 J/molK JEE Main 2024 (09 Apr Shift 2) JEE Main Previous Year Paper ): (1) 20 J (2) 205 J (3) −20 J (4) 225 J

Q7. A simple pendulum doing small oscillations at a place R height above earth surface has time period of T1 = 4 s . T2 would be it's time period if it is brought to a point which is at a height 2R from earth surface. Choose the correct relation [R = radius of earth ] : (1) 2 T1 = T2 (2) 2 T1 = 3 T2 (3) T1 = T2 (4) 3 T1 = 2 T2

Q8. A diatomic gas ( 𝛾= 1 . 4 ) does 200 J of work when it is expanded isobarically. The heat given to the gas in the process is : (1) 850 J (2) 800 J (3) 600 J (4) 700 J

Q8. Given below are two statements: Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation P1 −P2 = ρg (h2 −h1). Statement II : In ventury tube shown 2gh = v21 −v22 In the light of the above statements, choose the most appropriate answer from the options given below. (1) Both Statement I and Statement II are correct. (2) Statement I is correct but Statement II is incorrect. (3) Statement I is incorrect but Statement II is (4) Both Statement I and Statement II are incorrect. correct.

Q8. In hydrogen like system the ratio of coul0mbian force and gravitational force between an electron and a proton is in the order of : (1) 1039 (2) 1029 (3) 1019 (4) 1036

Q8. A sample of 1 mole gas at temperature T is adiabatically expanded to double its volume. If adiabatic constant for the gas is γ = 32 , then the work done by the gas in the process is: (1) R T [2 −√2] (2) RT [2 + √2] (3) RT [2 −√2] (4) RT[2 + √2]

Q8. Choose the correct statement for processes 𝐴 & 𝐵 shown in figure. (1) 𝑃𝑉𝛾= 𝑘 for process 𝐵 and 𝑃𝑉= 𝑘 for process 𝐴. (2) 𝑃𝑉= 𝑘 for process 𝐵 and 𝐴. 𝑃𝛾- 1 𝑇𝛾 (3) (4) 𝑘 for process 𝐵 and 𝑇= 𝑘 for process 𝐴. 𝑇𝛾= 𝑃𝛾- 1 = 𝑘 for process 𝐴 and 𝑃𝑉= 𝑘 for process 𝐵.

Q8. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute 𝐶𝑝 temperature. The ratio of for the gas is : 𝐶𝑣 (1) 5 (2) 3 3 2 7 9 (3) (4) 5 7

Q8. A thermodynamic system is taken from an original state A to an intermediate state B by a linear process as shown in the figure. Its volume is then reduced to the original value from B to C by an isobaric process. The total work done by the gas from A to B and B to C would be : JEE Main 2024 (29 Jan Shift 1) JEE Main Previous Year Paper (1) 33800 J (2) 2200 J (3) 600 J (4) 800 J

Q8. A small liquid drop of radius R is divided into 27 identical liquid drops. If the surface tension is T , then the work done in the process will be : (1) 8πR2T (2) 3πR2T (3) 1 πR2T (4) 4πR2T 8

Q8. 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 : JEE Main 2024 (06 Apr Shift 1) JEE Main Previous Year Paper (1) mg (1 −ρρ0) (2) mg (1 + ρ0ρ ) (3) mg ( ρ0ρ −1) (4) mg(1 −ρ0ρ ) ∇

Q8. A diatomic gas (γ = 1.4) does 100 J of work in an isobaric expansion. The heat given to the gas is : (1) 250 J (2) 150 J (3) 350 J (4) 490 J

Q8. 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) RT[1 −2√2] (2) RT[√2 −2] (3) RT[2 −√2] (4) RT[2√2 −1]

Q8. During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of CP for the gas is : CV JEE Main 2024 (05 Apr Shift 2) JEE Main Previous Year Paper (1) 5 (2) 9 3 7 (3) 3 (4) 7 2 5

Q8. Four identical particles of mass 𝑚 are kept at the four corners of a square. If the gravitational force exerted on 2√2 + 1 𝐺𝑚2 one of the masses by the other masses is , the length of the sides of the square is 32 𝐿2 𝐿 (1) (2) 4𝐿 2 (3) 3𝐿 (4) 2𝐿

Q8. At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47°C ? (1) 80 K (2) −73 K (3) 4 K (4) 20 K

Q8. A total of 48 J heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by 2∘C. The work done by the gas is: Given, R = 8.3 J K−1 mol−1 . JEE Main 2024 (06 Apr Shift 2) JEE Main Previous Year Paper (1) 24.9 J (2) 72.9 J (3) 48 J (4) 23.1 J