Practice Questions

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. 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 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. 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 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 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. 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 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

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. A gas mixture consists of 8 moles of argon and 6 moles of oxygen at temperature 𝑇. Neglecting all vibrational modes, the total internal energy of the system is (1) 29 𝑅𝑇 (2) 20 𝑅𝑇 (3) 27 𝑅𝑇 (4) 21 𝑅𝑇

Q8. The temperature of a gas is −78∘C and the average translational kinetic energy of its molecules is K. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2 K is : (1) 127∘C (2) 117∘C (3) −39∘C (4) −78∘C

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. 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 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]

Q9. The total kinetic energy of 1 mole of oxygen at 27°C is : [Use universal gas constant (R) = 8 . 31 J mol-1 K-1 ] (1) 6845 . 5 J (2) 5942 . 0 J (3) 6232 . 5 J (4) 5670 . 5 J

Q9.Match List I with List II : (1) (A)-(III), (B)-(IV), (C)-(I), (D)-(II) (2) (A)-(II), (B)-(I), (C)-(IV), (D)-(III) (3) (A)-(I), (B)-(II), (C)-(III), (D)-(IV) (4) (A)-(I), (B)-(IV), (C)-(II), (D)-(III)

Q9. Two thermodynamical process are shown in the figure. The molar heat capacity for process A and B are CA and CB . The molar heat capacity at constant pressure and constant volume are represented by CP and CV , respectively. Choose the correct statement. (1) CP > CB > CV (2) CA = 0 and CB = ∞ (3) CP > CV > CA = CB (4) CA > CP > CV

Q9. Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio Va and the ratio Vb is: Vd Vc (1) Va ≠Vb (2) Va = Vb Vd Vc Vd Vc (3) Va Vb −1 (4) Va Vb 2 = = Vd ( Vc ) Vd ( Vc )

Q9. The pressure and volume of an ideal gas are related as 𝑃𝑉 32 = 𝐾 (Constant). The work done when the gas is taken from state 𝐴𝑃1, 𝑉1, 𝑇1 to state 𝐵𝑃2, 𝑉2, 𝑇2 is : (1) 2 ( 𝑃1𝑉1 - 𝑃2𝑉2 ) (2) 2 ( 𝑃2𝑉2 - 𝑃1𝑉1 ) (3) 2√𝑃1𝑉1 −√𝑃2𝑉2 (4) 2𝑃2√𝑉2 −𝑃1√𝑉1

Q9. The translational degrees of freedom (ft) and rotational degrees of freedom (fr) of CH4 molecule are: (1) ft = 2 and fr = 2 (2) ft = 3 and fr = 3 (3) ft = 3 and fr = 2 (4) ft = 2 and fr = 3

Q9. The average kinetic energy of a monatomic molecule is 0. 414 eV at temperature: JEE Main 2024 (27 Jan Shift 1) JEE Main Previous Year Paper (Use KB = 1. 38 × 10−23 J mol−1 K−1 ) (1) 3000 K (2) 3200 K (3) 1600 K (4) 1500 K

Q9. Two vessels A and B are of the same size and are at same temperature. A contains 1 g of hydrogen and B contains 1 g of oxygen. PA and PB are the pressures of the gases in A and B respectively, then PA is : PB (1) 16 (2) 8 (3) 4 (4) 32

Q9. The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are 8Ω and 10Ω respectively. After inserting in a hot bath of temperature 400∘C , the resistance of platinum wire is : (1) 10Ω (2) 8Ω (3) 16Ω (4) 2Ω

Q9. The speed of sound in oxygen at S.T.P. will be approximately: (Given, 𝑅= 8 . 3 J K-1, 𝛾= 1 . 4) (1) 310 m s-1 (2) 333 m s-1 (3) 341 m s-1 (4) 325 m s-1