Practice Questions

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. 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 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. 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. 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 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. 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. 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. 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. 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

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. 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. 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. 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. 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 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

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. 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 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

Q10.A particle executes SHM of amplitude 𝐴. The distance from the mean position when its kinetic energy becomes equal to its potential energy is: (1) 1 (2) 2𝐴 √2𝐴 (3) √2𝐴 (4) 12𝐴

Q10.A fully loaded boeing aircraft has a mass of 5. 4 × 105 kg. Its total wing area is 500 m2 . It is in level flight with a speed of 1080 km h−1 . If the density of air ρ is 1. 2 kg m–3 , the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be ( g = 10 m s−2 ) (1) 16 (2) 6 (3) 8 (4) 10

Q10.The Young's modulus of a steel wire of length 6 m and cross-sectional area 3 mm2 , is 2 × 1111 N/m2 . The wire is suspended from its support on a given planet. A block of mass 4 kg is attached to the free end of the JEE Main 2023 (01 Feb Shift 2) JEE Main Previous Year Paper wire. The acceleration due to gravity on the planet is 1 of its value on the earth. The elongation of wire is 4 (Take g on the earth = 10 m/s2 ): (1) 1 cm (2) 1 mm (3) 0. 1 mm (4) 0. 1 cm

Q10.A particle executes S.H.M. of amplitude 𝐴 along 𝑥-axis. At 𝑡= 0, the position of the particle is 𝑥= and it 2 moves along positive 𝑥-axis. The displacement of particle in time 𝑡 is 𝑥= 𝐴 sin𝜔𝑡 + 𝛿, then the value 𝛿 will be (1) 𝜋 (2) 𝜋 2 6 𝜋 𝜋 (3) (4) 3 4