Practice Questions

Q7. A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is : (1) GmMπ2 (2) GMmπ L2 2 L2 (3) 0 (4) 2GmMπ L2

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 block of ice at -10 °C is slowly heated and converted to steam at 100 °C. Which of the following curves represent the phenomenon qualitatively: JEE Main 2024 (30 Jan Shift 2) JEE Main Previous Year Paper (1) (2) (3) (4)

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. 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 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. 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. 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. 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. 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. 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. 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. 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. With rise in temperature, the Young's modulus of elasticity (1) changes erratically (2) decreases (3) increases (4) remains unchanged

Q8. Correct Bernoulli's equation is (symbols have their usual meaning) : (1) P + mgh + 12 mv2 = constant (2) P + ρgh + 21 ρv2 = constant (3) P + ρgh + ρv2 = constant (4) P + 12 ρgh + 21 ρv2 = constant JEE Main 2024 (08 Apr Shift 1) JEE Main Previous Year Paper

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. 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. 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 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. 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. 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. 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. 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. 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.