Practice Questions

Q6. A water drop of radius 1 cm is broken into 729 equal droplets. If surface tension of water is 75 dyne cm−1 , then the gain in surface energy upto first decimal place will be [Given π = 3. 14 ] JEE Main 2022 (26 Jul Shift 1) JEE Main Previous Year Paper (1) 8. 5 × 10−4 J (2) 8. 2 × 10−4 J (3) 7. 5 × 10−4 J (4) 5. 3 × 10−4 J Q7. 7 mole of certain monoatomic ideal gas undergoes a temperature increase of 40 K at constant pressure. The increase in the internal energy of the gas in this process is (Given R = 8. 3 J K−1 mol−1 ) (1) 5810 J (2) 3486 J (3) 11620 J (4) 6972 J

Q6. The torque of a force 5 ^𝑖+ 3 ^𝑗- 7 ^𝑘 about the origin is 𝜏. If the force acts on a particle whose position vector is 2 ^𝑖+ 2 ^𝑗+ ^𝑘, then the value of 𝜏 will be (1) 11 ^𝑖+ 19 ^𝑗- 4 ^𝑘 (2) -11 ^𝑖+ 9 ^𝑗- 16 ^𝑘 (3) -17 ^𝑖+ 19 ^𝑗- 4 ^𝑘 (4) 17 ^𝑖+ 9 ^𝑗+ 16 ^𝑘

Q6. A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2 . Two smaller pieces fly off perpendicular to each other with velocities of 30 m s−1 and 40 m s−1 respectively. The velocity of the third piece will be (1) 35 m s−1 (2) 50 m s−1 (3) 25 m s−1 (4) 15 m s−1

Q6. A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0. 075 N m−1 . In this process the gain in surface energy will be (1) 2. 8 × 10−4 J (2) 1. 5 × 10−3 J (3) 1. 9 × 10−4 J (4) 9. 4 × 10−5 J

Q6. Two cylindrical vessels of equal cross-sectional area 16 cm2 contain water upto heights 100 cm and 150 cm respectively. The vessels are interconnected so that the water levels in them become equal. The work done by the force of gravity during the process, is [Take density of water = 103 kg m−3 and g = 10 ms−2 ] (1) 0. 25 J (2) 1 J (3) 8 J (4) 12 J JEE Main 2022 (27 Jul Shift 1) JEE Main Previous Year Paper

Q6. The approximate height from the surface of earth at which the weight of the body becomes 1 of its weight on 3 the surface of earth is : [Radius of earth R = 6400 km and √3 = 1. 732 ] (1) 3840 km (2) 4685 km (3) 2133 km (4) 4267 km

Q6. Two bodies of mass 1 kg and 3 kg have position vectors ˆi + 2ˆj + ˆk and −3ˆi −2ˆj + ˆk respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector : (1) ˆi −2ˆj + ˆk (2) −3ˆi −2ˆj + ˆk (3) −2ˆi + 2ˆk (4) −2ˆi −ˆj + 2ˆk

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. 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 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. 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. 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. 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. 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 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. 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 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 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 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. 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. 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. 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. 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. 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