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. 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 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. A thermodynamic system is taken through cyclic process. The total work done in the process is : JEE Main 2023 (15 Apr Shift 1) JEE Main Previous Year Paper (1) 200 J (2) 300 J (3) 100 J (4) Zero

Q8. Given below are two statements: Statement I: The temperature of a gas is -73 °C. When the gas is heated to 527 °C, the root mean square speed of the molecules is doubled. Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below: (1) Both Statement I and Statement II are true (2) Statement I is true but Statement II is false (3) Both Statement I and Statement II are false (4) Statement I is false but Statement II is true

Q8. A uniform disc of mass 0. 5 kg and radius r is projected with velocity 18 m s−1 at t = 0 s on a rough horizontal surface. It starts off with a purely sliding motion at t = 0 s. After 2 s it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after 2 s will be ______ J. (given, coefficient of friction is 0. 3 and g = 10 m s−2 ).

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 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. 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. Given below are two statements: Statement I: If E be the total energy of a satellite moving around the earth, then its potential energy will be E . 2 Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy E . In the light of the above statements, choose the most appropriate answer from the options given below. (1) Statement I is correct but Statement II is incorrect (2) Statement I is incorrect but Statement II is correct (3) Both Statement I and Statement II are correct (4) Both Statement I and Statement II are incorrect

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. 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. 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 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. 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. 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. Choose the incorrect statement from the following: JEE Main 2023 (06 Apr Shift 2) JEE Main Previous Year Paper (1) The speed of satellite in a given circular orbit (2) For a planet revolving around the sun in an remains constant elliptical orbit, the total energy of the planet remains constant (3) The linear speed of a planet revolving around the (4) When a body falls towards earth, the sun remains constant displacement of earth towards the body is negligible

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. 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. A planet having mass 9 Me and radius 4Re, where Me and Re are mass and radius of earth respectively, has escape velocity in km s−1 given by: (Given escape velocity on earth Ve = 11. 2 × 103 m s−1 ) (1) 67. 2 (2) 16. 8 (3) 11. 2 (4) 33. 6

Q8. The initial pressure and volume of an ideal gas are 𝑃0 and 𝑉0. The final pressure of the gas when the gas is suddenly compressed to volume 𝑉0 will be: 4 (Given 𝛾= ratio of specific heats at constant pressure and at constant volume.) (1) 𝑃0 ( 4 ) 𝛾 (2) 4𝑃0 1 𝛾 (3) 𝑃0 (4) 𝑃0 ( 4 )

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. The height of liquid column raised in a capillary tube of certain radius when dipped in liquid 𝐴 vertically is, 5 cm. If the tube is dipped in a similar manner in another liquid 𝐵 of surface tension and density double the JEE Main 2023 (30 Jan Shift 1) JEE Main Previous Year Paper values of liquid 𝐴, the height of liquid column raised in liquid B would be ______ m. (1) 0 . 20 (2) 0 . 5 (3) 0 . 05 (4) 0 . 10

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

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