Practice Questions

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. 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. 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. 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

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. 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. 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. Statement - I : When μ amount of an ideal gas undergoes adiabatic change from state (P1, V1, T1) to state μR(T2−T1) CP (P2, V2, T2), then work done is W = 1−γ , where γ = CV and R = universal gas constant. JEE Main 2022 (28 Jun Shift 1) JEE Main Previous Year Paper Statement - II : In the above case, when work is done on the gas, the temperature of the gas would rise. (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.

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 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. 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 steel wire of length 3. 2 m(YS = 2. 0 × 1011 N m−2) and a copper wire of length 4. 4 m (YC = 1. 1 × 1011 N m−2) , both of radius 1. 4 mm are connected end to end. When stretched by a load, the net elongation is found to be 1. 4 mm. The load applied, in Newton, will be: (Given π = 227 ) (1) 360 (2) 180 (3) 1080 (4) 154

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. 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. Statement I : The law of gravitation holds good for any pair of bodies in the universe. Statement II : The weight of any person becomes zero when the person is at the centre of the earth. In the light of the above statements, choose the correct answer from the options given below. JEE Main 2022 (27 Jun Shift 1) JEE Main Previous Year Paper (1) Statement 1 and statement 2 both are true. (2) Statement 1 is true and statement 2 is false. (3) Statement 1 and statement 2 both are false. (4) Statement 1 is false and statement 2 is true.

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. The efficiency of a Carnot's engine, working between steam point and ice point, will be (1) 26. 81% (2) 37. 81% (3) 47. 81% (4) 57. 81%

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. 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

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. Read the following statements : A . When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice. B. Two bodies P and Q having equal surface areas are maintained at temperature 10°C and 20°C . The thermal radiation emitted in a given time by P and Q are in the ratio 1 : 1. 15 C. A carnot Engine working between 100 K and 400 K has an efficiency of 75% D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice. Choose the correct answer from the options given below : (1) A, B, C only (2) A, B only (3) A, C only (4) B, C, D only

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. 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