Practice Questions

Q8. The velocity of a small ball of mass m and density d1 , when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is d2 , then the viscous force acting on the ball, will be (1) mg(1 −d1d2 ) (2) mg(1 −d2d1 ) (3) mg( d1d2 −1) (4) mg( d2d1 −1)

Q8. A thermodynamic system is taken from an original state 𝐷 to an intermediate state 𝐸 by the linear process shown in the figure. Its volume is then reduced to the original volume from 𝐸 to 𝐹 by an isobaric process. The total work done by the gas from 𝐷 to 𝐸 to 𝐹 will be (1) -450 J (2) 450 J (3) 900 J (4) 1350 J

Q8. A gas has 𝑛 degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be 𝑛 𝑛+ 2 (1) (2) 𝑛+ 2 𝑛 (3) 𝑛 (4) 𝑛 2𝑛+ 2 𝑛- 2

Q8. In the figure, a very large plane sheet of positive charge is shown. 𝑃1 and 𝑃2 are two points at distance 𝑙 and 2𝑙 from the charge distribution. If 𝜎 is the surface charge density, then the magnitude of electric fields 𝐸1 and 𝐸2 at 𝑃1 and 𝑃2 respectively are JEE Main 2022 (25 Jun Shift 1) JEE Main Previous Year Paper 𝜎 𝜎 2𝜎 𝜎 (1) 𝐸1 = 𝜀𝑜, 𝐸2 = 2𝜀𝑜 (2) 𝐸1 = 𝜀𝑜, 𝐸2 = 𝜀𝑜 𝜎 𝜎 (3) 𝐸1 = 𝐸2 = (4) 𝐸1 = 𝐸2 = 2𝜀𝑜 𝜀𝑜

Q8. Starting with the same initial conditions, an ideal gas expands from volume V1 to V2 in three different ways. The work done by the gas is W1 if the process is purely isothermal, W2 , if the process is purely adiabatic and W3 if the process is purely isobaric. Then, choose the correct option (1) W2 < W1 < W3 (2) W1 < W2 < W3 (3) W2 < W3 < W1 (4) W3 < W1 < W2

Q8. Following statements are given (1) The average kinetic energy of a gas molecule decreases when the temperature is reduced. (2) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature. (3) The average kinetic energy of a gas molecule decreases with increases in volume. (4) Pressure of a gas increases with increase in temperature at constant volume. (5) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below : (1) (1) and (4) only (2) (1), (2) and (4) only (3) (2) and (4) only (4) (1), (2) and (5) only

Q8. A vessel contains 14 g of nitrogen gas at a temperature of 27°C. The amount of heat to be transferred to the gas to double the r.m.s. speed of its molecules will be : (Take R = 8. 32 J mol−1 k−1 ) (1) 2229 J (2) 5616 J (3) 9360 J (4) 13, 104 J

Q8. The escape velocity of a body on a planet A is 12 km s−1 . The escape velocity of the body on another planet B, whose density is four times and radius is half of the planet A , is (1) 12 km s−1 (2) 24 km s−1 (3) 36 km s−1 (4) 6 km s−1

Q8. A drop of liquid of density ρ is floating half immersed in a liquid of density σ and surface tension 7. 5 × 10−4 N cm−1 . The radius of drop in cm will be : (Take : g = 10 ms−2 ) (1) 15 (2) 15 √2ρ−σ √ρ−σ (3) 3 (4) 3 2√ρ−σ 20√2ρ−σ

Q8. Given below are two statements: Statement I :The average momentum of a molecule in a sample of an ideal gas depends on temperature. JEE Main 2022 (28 Jul Shift 1) JEE Main Previous Year Paper Statement II : The rms speed of oxygen molecules in a gas is 𝑣. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become 2𝑣. 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) 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 2𝜋

Q8. A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1. 4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by : ( R = universal gas constant) (1) Mv2 (2) Mv2 7R 5R (3) 2 Mv27R (4) 7 Mv25R

Q8. Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Clothes containing oil or grease stains cannot be cleaned by water wash. Reason (R) : Because the angle of contact between the oil/ grease and water is obtuse. In the light of the above statements, choose the correct answer from the option given below. (1) Both (A) and (R) are true and (R) is the correct (2) Both (A) and (R) are true but (R) is not the explanation of (A) correct explanation of (A) (3) (A) is true but (R) is false (4) (A) is true but (R) is true

Q8. In 1stmsup case, Carnot engine operates between temperatures 300 K and 100 K . In 2ndmsup case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in 2ndmsup case) will be : JEE Main 2022 (27 Jul Shift 2) JEE Main Previous Year Paper (1) same as the 1st case (2) always greater than the 1st case (3) always less than the 1st case (4) may increase or decrease with respect to the 1st case

Q8. Two metallic plates form a parallel plate capacitor. The distance between the plate is '𝑑'. A metal sheet of 𝑑 thickness and of area equal to area of each plate is introduced between the plates. What will be the ratio of the 2 JEE Main 2022 (25 Jun Shift 2) JEE Main Previous Year Paper new capacitance to the original capacitance of the capacitor? (1) 1: 2 (2) 2: 1 (3) 1: 4 (4) 4: 1

Q8. A Carnot engine takes 5000 kcal of heat from a reservoir at 727°C and gives heat to a sink at 127°C. The work done by the engine is (1) 3 × 106J (2) Zero (3) 8. 4 × 106 J (4) 12. 6 × 106 J

Q8. A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is (Given, initial temperature of the bullet = 127°C, Melting point of the bullet = 327°C, Latent heat of fusion of lead = 2. 5 × 104 J kg−1 , Specific heat capacity of lead = 125 J kg K−1 ) (1) 125 m s−1 (2) 500 m s−1 (3) 250 m s−1 (4) 600 m s−1

Q8. A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be (1) P (2) 8P (3) 32P (4) 64P

Q8. For a specific wavelength 670 nm of light coming from a galaxy moving with velocity v, the observed wavelength is 670. 7 nm. The value of v is (1) 3 × 108 m s−1 (2) 3. 13 × 105 m s−1 (3) 3 × 1010 m s−1 (4) 4. 48 × 105 m s−1

Q9. Sixty four conducting drops each of radius 0. 02 m and each carrying a charge of 5 μC are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be (1) 1 : 4 (2) 4 : 1 (3) 1 : 8 (4) 8 : 1

Q9. A transverse wave is represented by 𝑦= 2sin𝜔𝑡- 𝑘𝑥cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be (1) 4𝜋 (2) 2𝜋 (3) 𝜋 (4) 2

Q9. Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is 1 : 4, then A . The r.m.s. velocity of gas molecules in two vessels will be the same. B. The ratio of pressure in these vessels will be 1 : 4 . C. The ratio of pressure will be 1 : 1 . D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of 1 : 4 . (1) A and C only (2) B and D only (3) A and B only (4) C and D only

Q9. For a perfect gas, two pressures P1 and P2 are shown in figure. The graph shows (1) P1 > P2 (2) P1 < P2 (3) P1 = P2 (4) Insufficient data to draw any conclusion

Q9. A Carnot engine whose heat sinks at 27°C, has an efficiency of 25%. By how many degrees should the temperature of the source be changed to increase the efficiency by 100% of the original efficiency ? (1) Increases by 18°C (2) Increases by 200°C (3) Increases by 120°C (4) Increases by 73°C

Q9. The root mean square speed of smoke particles of mass 5 × 10-17 kg in their Brownian motion in air at NTP is approximately. [Given 𝑘= 1 . 38 × 10-23J K-1] (1) 60 mm s-1 (2) 12 mm s-1 (3) 15 mm s-1 (4) 36 mm s-1

Q9. A mixture of hydrogen and oxygen has volume 2000 cm3 , temperature 300 K, pressure 100 kPa and mass 0. 76 g . The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be [Take gas constant R = 8. 3 J K−1 mol−1 ] (1) 1 (2) 3 3 1 (3) 1 (4) 16 16 1