Practice Questions

Q8. The acceleration due to gravity at height h above the earth if h ≪R (Radius of earth) is given by − 2R2 (1) g′ = g(1 h2 ) (2) g′ = g(1 − 2Rh ) (3) g′ = g(1 −2hR ) (4) g′ = g(1 −2h2R2 )

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)

Q8. Identify the correct statements from the following: (A) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative (B) Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative (C) Work done by friction on a body sliding down an inclined plane is positive (D) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero (E) Work done by the air resistance on an oscillating pendulum is negative Choose the correct answer from the options given below: (1) B and E only (2) A and C only (3) B, D and E only (4) B and D only

Q8. A sample of gas at temperature 𝑇 is adiabatically expanded to double its volume. The work done by the gas in 3 the process is given, (given 𝛾= 2) : - 2 (1) 𝑊= 𝑇𝑅√2 - 2 (2) 𝑊= 𝑅√2𝑇 𝑅 (3) 𝑊= 𝑇2 - √2 (4) 𝑊= 𝑅𝑇2 - √2

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. The ratio of escape velocity of a planet to the escape velocity of earth will be:- Given: Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth. JEE Main 2023 (12 Apr Shift 1) JEE Main Previous Year Paper (1) 4 : 1 (2) 1 : 4 (3) 1 : √2 (4) 2 : 1 Q9. 64 identical drops each charged upto potential of 10 mV are combined to form a bigger drop. The potential of the bigger drop will be _____ mV .

Q8. A body weight W , is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be: (1) W (2) W 91 100 (3) W (4) W 9 3

Q8. A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature 𝑇. Neglecting all vibrational modes, the total internal energy of the system will be: JEE Main 2023 (10 Apr Shift 2) JEE Main Previous Year Paper (1) 11𝑅𝑇 (2) 8𝑅𝑇 (3) 4𝑅𝑇 (4) 16𝑅𝑇

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. 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. 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

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. A flask contains Hydrogen and Argon in the ratio 2 : 1 by mass. The temperature of the mixture is 30°C . The ratio of average kinetic energy per molecule of the two gases ( KhydrogenKargon ) is: (Given : Atomic Weight of Ar = 39. 9 ) (1) 2 (2) 1 (3) 39. 9 (4) 39.92

Q9. Heat is given to an ideal gas in an isothermal process. A. Internal energy of the gas will decrease. B. Internal energy of the gas will increase. C. Internal energy of the gas will not change. D. The gas will do positive work. E. The gas will do negative work. Choose the correct answer from the options given below : (1) A and E only (2) B and D only (3) C and E only (4) C and D only

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. 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. The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become. (1) 4 hours (2) 6 hours (3) 12 hours (4) 3 hours

Q9. Every planet revolves around the sun in an elliptical orbit : A. The force acting on a planet is inversely proportional to square of distance from sun. B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun. C. The centripetal force acting on the planet is directed away from the sun. D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit. Choose the correct answer from the options given below : (1) A and D only (2) C and D only (3) B and C only (4) A and C only

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. A source supplies heat to a system at the rate of 1000 W . If the system performs work at a rate of 200 W . The rate at which internal energy of the system increases is (1) 600 W (2) 800 W (3) 500 W (4) 1200 W

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. A hydraulic automobile lift is designed to lift vehicles of mass 5000 kg. The area of cross section of the cylinder carrying load is 250 cm2 . The maximum pressure the smaller piston would have to bear is [Assume g = 10 m s−2 ] (1) 20 × 106 Pa (2) 2 × 105 Pa (3) 200 × 106 Pa (4) 2 × 106 Pa

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