Practice Questions

Q6. The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be : (1) √3 yr (2) 3√3 yr (3) 3 yr (4) 9 yr

Q6. Three identical particle 𝐴, 𝐵 and 𝐶 of mass 100 kg each are placed in a straight line with 𝐴𝐵= 𝐵𝐶= 13 m. The gravitational force on a fourth particle 𝑃 of the same mass is 𝐹, when placed at a distance 13 m from the particle 𝐵 on the perpendicular bisector of the line 𝐴𝐶. The value of 𝐹 will be approximately (1) 21G (2) 100G (3) 59G (4) 42G

Q7. If K1 and K2 are the thermal conductivities L1 and L2 are the lengths and A1 and A2 are the cross sectional areas of steel and copper rods respectively such that K2 = 9, A1 = 2, L1 = 2 . Then, for the arrangement as K1 A2 L2 shown in the figure. The value of temperature T of the steel - copper junction in the steady state will be (1) 18°C (2) 14°C (3) 45°C (4) 150°C

Q7. An object is taken to a height above the surface of earth at a distance 5 R from the centre of the earth. Where 4 radius of earth, R = 6400 km. The percentage decrease in the weight of the object will be JEE Main 2022 (25 Jul Shift 2) JEE Main Previous Year Paper (1) 36% (2) 50% (3) 64% (4) 25%

Q7. An ice cube of dimensions 60 cm × 50 cm × 20 cm is placed in an insulation box of wall thickness 1 cm. The box keeping the ice cube at 0°C of temperature is brought to a room of temperature 40°C. The rate of melting of ice is approximately: (Latent heat of fusion of ice is 3 . 4 × 105 J kg-1 and thermal conducting of insulation wall is 0 . 05 W m-1 °C-1) JEE Main 2022 (26 Jul Shift 2) JEE Main Previous Year Paper (1) 61 × 10-1 kg s-1 (2) 61 × 10-5 kg s-1 (3) 208 kg s-1 (4) 30 × 10-5 kg s-1

Q7. A 100 g of iron nail is hit by a 1. 5 kg hammer striking at a velocity of 60 ms−1 . What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail ? [Specific heat capacity of iron = 0. 42 Jg−1 ∘C−1 ] (1) 16. 07°C (2) 6. 75°C (3) 1600°C (4) 675°C

Q7. At what temperature a gold ring of diameter 6. 230 cm be heated so that it can be fitted on a wooden bangle of diameter 6. 241 cm ? Both the diameters have been measured at room temperature (27°C) . (Given: coefficient of linear thermal expansion of gold αL = 1. 4 × 10−5 K−1 ) (1) 125. 7°C (2) 91. 7°C (3) 425. 7°C (4) 152. 7°C

Q7. A water drop of radius 1μm falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is 1. 8 × 10−5 N s m−2 and its density is negligible as compared to that of water 106 g m−3 . Terminal velocity of the water drop is (Take acceleration due to gravity = 10 m s−2 ) (1) 145. 4 × 10−6 m s−1 (2) 123. 4 × 10−6 m s−1 (3) 118. 0 × 10−6 m s−1 (4) 132. 6 × 10−6 m s−1

Q7. If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modulus of the material of the wire will : (1) Remain same (2) Become 8 times its initial value (3) Become 1th of its initial value (4) Become 4 times its initial value 4

Q7. The relation between root mean square speed 𝑣rms and most probable speed 𝑣p for the molar mass 𝑀 of oxygen gas molecule at the temperature of 300 K will be 2 1 (1) (2) 𝑣rms = √ 𝑣rms = √ 3𝑣p 3𝑣p 3 (3) (4) 𝑣rms = 𝑣p 𝑣rms = √ 2𝑣p

Q7. The bulk modulus of a liquid is 3 × 1010 Nm−2 . The pressure required to reduce the volume of liquid by 2% is : (1) 3 × 108 N m−2 (2) 6 × 108 N m−2 (3) 9 × 108 N m−2 (4) 12 × 108 N m−2

Q7. The ratio of specific heats in terms of degree of freedom 𝑓 is given by : 𝐶𝑉 (1) 1 + 𝑓 (2) 1 + 2 3 𝑓 (3) 1 + 𝑓 (4) 1 + 1 2 𝑓

Q7. A Carnot engine has efficiency of 50%. If the temperature of sink is reduced by 40°C, its efficiency increases by 30%. The temperature of the source will be : (1) 166 . 7 K (2) 255 . 1 K (3) 266 . 7 K (4) 367 . 7 K

Q7. A spherical shell of 1 kg mass and radius R is rolling with angular speed ω on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is a R2ω. The value of a will be 3 JEE Main 2022 (29 Jun Shift 1) JEE Main Previous Year Paper (1) 2 (2) 3 (3) 5 (4) 4

Q7. Four spheres each of mass m form a square of side d (as shown in figure). A fifth sphere of mass M is situated at the centre of square. The total gravitational potential energy of the system is + + + + (1) −Gmd [(4 √2)m 4√2M] (2) −Gmd [(4 √2)M 4√2m] + + (3) −Gmd [3m2 4√2M] (4) −Gmd [6m2 4√2M] JEE Main 2022 (27 Jun Shift 2) JEE Main Previous Year Paper

Q7. An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, 𝑔= 10 m s-2 and radius of earth = 6400 km] JEE Main 2022 (29 Jul Shift 2) JEE Main Previous Year Paper (1) 48MJ (2) 24MJ (3) 36MJ (4) 12MJ

Q7. Consider a cylindrical tank of radius 1 m is filled with water. The top surface of water is at 15 m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5 m from the bottom. A force of 5 × 105 N is applied an the top surface of water using a piston. The speed of efflux from the hole will be : (given atmospheric pressure PA = 1. 01 × 105 Pa, density of water ρw = 1000 kg m−3 and gravitational acceleration g = 10 m s−2 ) (1) 11. 6 m s−1 (2) 10. 8 m s−1 (3) 17. 8 m s−1 (4) 14. 4 m s−1

Q7. A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27°C . The ratio of their average kinetic energy per molecule respectively (1) 3 : 5 (2) 9 : 4 (3) 2 : 3 (4) 1 : 1

Q7. A certain amount of gas of volume 𝑉 at 27°C temperature and pressure 2 × 107N m-2 expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use 𝛾= 1 . 5) (1) 3 . 536 × 105 Pa (2) 3 . 536 × 106 Pa (3) 1 . 25 × 106 Pa (4) 1 . 25 × 105 Pa JEE Main 2022 (25 Jul Shift 1) JEE Main Previous Year Paper

Q8. Resistance of the wire is measured as 2 Ω and 3 Ω at 10°C and 30°C respectively. Temperature coefficient of resistance of the material of the wire is (1) 0. 033∘C−1 (2) −0. 033∘C−1 (3) 0. 011∘C−1 (4) 0. 055°C−1

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. 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. A radar sends an electromagnetic signal of electric field (E0) = 2. 25 V m−1 and magnetic field (B0) = 1. 5 × 10−8 T which strikes a target on line of sight at a distance of 3 km in a medium. After that, a part of signal (echo) reflects back towards the radar with same velocity and by same path. If the signal was transmitted at time t = 0 from radar, then after how much time echo will reach to the radar? (1) 2. 0 × 10−5 s (2) 4. 0 × 10−5 s (3) 1. 0 × 10−5s (4) 8. 0 × 10−5s

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