Practice Questions

Q6. The force required to stretch a wire of cross-section 1 cm2 to double its length will be : (Given Yong's modulus of the wire = 2 × 1011 N m-2) (1) 1 × 107 N (2) 1 . 5 × 107 N (3) 2 × 107 N (4) 2 . 5 × 107 N

Q6. What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on elastic collision) (1) 50. 0% (2) 66. 6% (3) 55. 6% (4) 33. 3%

Q6. A body of mass m is projected with velocity λve in vertically upward direction from the surface of the earth into space. It is given that ve is escape velocity and λ < 1 . If air resistance is considered to the negligible, then the maximum height from the centre of earth, to which the body can go, will be ( R : radius of earth) (1) R (2) R 1+λ2 1−λ2 (3) R (4) λ2R 1−λ 1−λ2

Q6. The length of a seconds pendulum at a height h = 2R from earth surface will be: (Given: R = Radius of earth and acceleration due to gravity at the surface of earth g = π2 m s−2 ) (1) 9 2 m (2) 49 m (3) 8 9 m (4) 19 m

Q6. The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be (1) 36 hours (2) 40 hours (3) 30 hours (4) 25 hours JEE Main 2022 (29 Jun Shift 2) JEE Main Previous Year Paper

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. 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. 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

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. 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. 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. 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. 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. 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. 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. 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 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. 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 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. 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 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 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 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. 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. 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