Practice Questions

Q8. The pressure of a gas changes linearly with volume from 𝐴 to 𝐵 as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be (1) 6 J (2) Zero (3) -4 . 5 J (4) 4 . 5 J 𝐶𝑃

Q8. The escape velocities of two planets A and B are in the ratio 1 : 2 . If the ratio of their radii respectively is 1 : 3 , then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be: (1) 4 (2) 3 3 2 (3) 2 (4) 3 3 4

Q8. Consider two containers 𝐴 and 𝐵 containing monoatomic gases at the same Pressure 𝑃, Volume 𝑉 and 1 Temperature 𝑇. The gas in 𝐴 is compressed isothermally to of its original volume while the gas in 𝐵 is 8 compressed adiabatically to 1 of its original volume. The ratio of final pressure of gas in 𝐵 to that of gas in 𝐴 is 8 (1) 8 (2) 4 3 1 (3) (4) 8 2 8

Q8. Two particles of equal mass m move in a circle of radius r under the action of their mutual gravitational attraction. The speed of each particle will be : (1) √Gm2r (2) √4Gmr (3) √Gmr (4) √Gm4r

Q8. Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g . The time period of the motion of the particle will be (approximately) (take g = 10 ms−2 , radius of earth = 6400 km) JEE Main 2023 (25 Jan Shift 1) JEE Main Previous Year Paper (1) 24 hours (2) 1 hour 24 minutes (3) 1 hour 40 minutes (4) 12 hours

Q8. Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed 𝑣𝑟𝑚𝑠 and choose the correct answer from the options given below: (1) v𝑟𝑚𝑠( mono ) > v𝑟𝑚𝑠( dia ) > v𝑟𝑚𝑠( poly ) (2) V𝑟𝑚𝑠( mono ) = V𝑟𝑚𝑠( dia ) = V𝑟𝑚𝑠( poly ) (3) v𝑟𝑚𝑠( mono ) < v𝑟𝑚𝑠( dia ) < v𝑟𝑚𝑠( poly ) (4) v𝑟𝑚𝑠( dia ) < v𝑟𝑚𝑠( poly ) < v𝑟𝑚𝑠( mono )

Q8. A small ball of mass 𝑀 and density 𝜌 is dropped in a viscous liquid of density 𝜌0. After some time, the ball falls with a constant velocity. What is the viscous force on the ball? 𝜌0 𝜌 (1) 𝐹= 𝑀𝑔1 + (2) 𝐹= 𝑀𝑔1 + 𝜌 𝜌0 𝜌0 (3) 𝐹= 𝑀𝑔1 - (4) 𝐹= 𝑀𝑔1 ± 𝜌𝜌0 𝜌

Q8. A body of mass is taken from earth surface to the height h equal to twice the radius of earth (Re), the increase in potential energy will be : ( g = acceleration due to gravity on the surface of earth) (1) 3mgRe (2) 31 mgRe (3) 2 3 mgRe (4) 12 mgRe

Q8. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: A pendulum clock when taken to Mount Everest becomes fast. Reason R: The value of g (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth. In the light of the above statements, choose the most appropriate answer from the options given below (1) Both A and R are correct and R is the correct (2) Both A and R are correct but R is not the correct explanation of A explanation of A (3) A is correct but R is not correct (4) A is not correct but R is correct

Q8. A space ship of mass 2 × 104 kg is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if g = 10 m s−2 and radius of earth = 6400 km ): km s−1 (1) 11. 2(√2 −1) km s−1 (2) 8(√2 −1) km s−1 (3) 7. 9(√2 −1) km s−1 (4) 7. 4(√2 −1)

Q9. Under isothermal condition, the pressure of a gas is given by P = aV –3, where a is a constant and V is the volume of the gas. The bulk modulus at constant temperature is equal to (1) 3P (2) P (3) 2P (4) P2

Q9. The correct relation between 𝛾= and temperature 𝑇 is : 𝐶𝑉 (1) 𝛾∝ 1 (2) 𝛾∝𝑇0 √𝑇 (3) 𝛾∝1 (4) 𝛾∝𝑇 𝑇

Q9. A travelling wave is described by the equation 𝑦𝑥, 𝑡= 0 . 05sin8𝑥- 4𝑡 m. The velocity of the wave is: [All the quantities are in SI unit] (1) 4 m s-1 (2) 2 m s-1 (3) 0 . 5 m s-1 (4) 8 m s-1

Q9. Match List I with List II: List I List II (A)3 Translational degrees of freedom (I) Monoatomic gases (B) 3 Translational, 2 rotational degrees of freedoms (II) Polyatomic gases 3 Translational, 2 rotational and 1 vibrational degrees Rigid diatomic (C) (III) of freedom gases (D)3 Translational, 3 rotational and more than one (IV)Nonrigid diatomic vibrational degrees of freedom gases Choose the correct answer from the options given below: (1) A - I, B - III, C - IV, D - II (2) A - IV, B - III, C - II, D - I (3) A - IV, B - II, C - I, D - III (4) A - I, B - IV, C - III, D - II 𝐴

Q9. Eight equal drops of water are falling through air with a steady speed of 10 cm s−1 . If the drops coalesce, the new velocity is:- (1) 16 cm s−1 (2) 40 cm s−1 (3) 5 cm s−1 (4) 10 cm s−1 JEE Main 2023 (11 Apr Shift 2) JEE Main Previous Year Paper

Q9. A metal block of mass m is suspended from a rigid support through a metal wire of diameter 14 mm. The tensile stress developed in the wire under equilibrium state is 7 × 105 N m–2 . The value of mass m is ______ kg. (Take g = 9. 8 m s−2 and π = 227 )

Q9. Surface tension of a soap bubble is 2. 0 × 10−2 N m−1 . Work done to increase the radius of soap bubble from 3. 5 cm to 7 cm will be : [Take π = 227 ] (1) 0. 72 × 10−4 J (2) 5. 76 × 10−4 J (3) 18. 48 × 10−4 J (4) 9. 24 × 10−4 J JEE Main 2023 (29 Jan Shift 1) JEE Main Previous Year Paper

Q9. The weight of a body on the earth is 400 N. Then weight of the body when taken to a depth half of the radius of the earth will be: (1) 200 N (2) Zero (3) 100 N (4) 300 N

Q9. Under the same load, wire A having length 5. 0 m and cross section 2. 5 × 10−5 m2 stretches uniformly by the same amount as another wire B of length 6. 0 m and a cross section of 3. 0 × 10−5 m2 stretches. The ratio of the JEE Main 2023 (31 Jan Shift 2) JEE Main Previous Year Paper Young's modulus of wire A to that of wire B will be: (1) 1 : 4 (2) 1 : 1 (3) 1 : 10 (4) 1 : 2

Q9. The mean free path of molecules of a certain gas at STP is 1500𝑑, where 𝑑 is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373 𝐾 is approximately: JEE Main 2023 (13 Apr Shift 2) JEE Main Previous Year Paper (1) 750𝑑 (2) 1098𝑑 (3) 2049𝑑 (4) 1500𝑑

Q9. T is the time period of simple pendulum on the earth's surface. Its time period becomes xT when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of x will be: (1) 4 (2) 2 (3) 1 (4) 1 2 4

Q9. If the distance of the earth from Sun is 1. 5 × 106 km, then the distance of an imaginary planet from Sun, if its period of revolution is 2. 83 years is: (1) 6 × 107 km (2) 6 × 106 km (3) 3 × 106 km (4) 3 × 107 km

Q9. A force is applied to a steel wire A , rigidly clamped at one end. As a result elongation in the wire is 0. 2 mm. If same force is applied to another steel wire B of double the length and a diameter 2. 4 times that of the wire A, the elongation in the wire B will be (wires having uniform circular cross sections) (1) 6. 06 × 10–2 mm (2) 2. 77 × 10–2 mm (3) 3. 0 × 10–2 mm (4) 6. 9 × 10–2 mm

Q10.In a linear Simple Harmonic Motion (SHM) (A) Restoring force is directly proportional to the displacement. (B) The acceleration and displacement are opposite in direction. (C) The velocity is maximum at mean position. (D) The acceleration is minimum at extreme points. Choose the correct answer from the options given below: (1) (C) and (D) only (2) (A), (C) and (D) only (3) (A), (B) and (C) only (4) (A), (B) and (D) only

Q10.The surface tension of soap solution is 3. 5 × 10−2 N m−1 . The amount of work done required to increase the radius of soap bubble from 10 cm to 20 cm is _____ ×10−4 J . (take π = 227 )