Practice Questions

Q8. A diatomic gas, having CP = 72 R and CV = 52 R, is heated at constant pressure. The ratio dU : dQ : dW (1) 3 : 5 : 2 (2) 5 : 7 : 3 (3) 5 : 7 : 2 (4) 3 : 7 : 2

Q8. The normal density of a material is ρ and its bulk modulus of elasticity is K . The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be : (1) PKρ (2) ρPK (3) ρKP (4) ρPK

Q8. A reversible engine has an efficiency of 1 . If the temperature of the sink is reduced by 58°C, its efficiency 4 becomes double. Calculate the temperature of the sink: (1) 180. 4°C (2) 382°C (3) 174 K (4) 280°C

Q8. A balloon carries a total load of 185 kg at normal pressure and temperature of 27°C. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is −7°C. Assuming the volume constant? (1) 214. 15 kg (2) 123. 54 kg (3) 219. 07 kg (4) 181. 46 kg JEE Main 2021 (27 Aug Shift 1) JEE Main Previous Year Paper

Q8. A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount of heat energy supplied to the engine from the source in each cycle is: (1) 3200 J (2) 1800 J (3) 1600 J (4) 2400 J

Q8. In the experiment of Ohm's law, a potential difference of 5. 0 V is applied across the end of a conductor of length 10. 0 cm and diameter of 5. 00 mm. The measured current in the conductor is 2. 00 A. The maximum permissible percentage error in the resistivity of the conductor is :- (1) 3. 9 (2) 8. 4 (3) 7. 5 (4) 3. 0

Q8. A mass of 50 kg is placed at the center of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the center is V kg m−1 . The value of V is: (1) +2G (2) −20G (3) −4G (4) −60G

Q8. The temperature of equal masses of three different liquids x, y and z are 10°C, 20°C and 30°C respectively. The temperature of mixture when x is mixed with y is 16°C and that when y is mixed with z is 26°C. The temperature of mixture when x and z are mixed will be : (1) 25. 62°C (2) 20. 28°C (3) 28. 32°C (4) 23. 84°C

Q8. Two thin metallic spherical shells of radii 𝑟1 and 𝑟2𝑟1 < 𝑟2 are placed with their centres coinciding. A material of thermal conductivity 𝐾 is filled in the space between the shells. The inner shell is maintained at temperature 𝜃1 and the outer shell at temperature 𝜃2𝜃1 < 𝜃2 . The rate at which heat flows radially through the material is : (1) 𝐾𝜃2 - 𝜃1 (2) 𝐾𝜃2 - 𝜃1𝑟2 - 𝑟1 𝑟2 - 𝑟1 4𝜋𝑟1𝑟2 (3) 𝜋𝐾𝑟1𝑟2𝜃2 - 𝜃1 (4) 4𝜋𝐾𝑟1𝑟2𝜃2 - 𝜃1 𝑟2 - 𝑟1 𝑟2 - 𝑟1

Q8. Y = A sin(ωt + ϕ0) is the time-displacement equation of a SHM. At t = 0 the displacement of the particle is Y = A2 and it is moving along negative x-direction. Then the initial phase angle ϕ0 will be: (1) 2π (2) π 3 6 (3) 5π (4) π 6 3 →

Q9. The internal energy (U), pressure (P) and volume (V ) of an ideal gas are related as U = 3PV + 4. The gas is (1) either monoatomic or diatomic (2) polyatomic only (3) monoatomic only (4) diatomic only

Q9. Due to cold weather, a 1 m water pipe of cross-sectional area 1 cm2 is filled with ice at -10 °C . Resistive heating is used to melt the ice. Current of 0 . 5 A is passed through 4 kΩ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required? (Given latent heat of fusion for water/ice = 3 . 33 × 105 J kg-1, specific heat of ice = 2 × 103 J kg-1 °C-1 and density of ice = 103 kg m-3 ) (1) 3 . 53 s (2) 0 . 353 s (3) 35 . 3 s (4) 70 . 6 s

Q9. The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy 2 × 10−9 J per molecule is: (1) 0. 75 × 1011 (2) 3 × 1011 (3) 1. 5 × 1011 (4) 6 × 1011

Q9. Two spherical soap bubbles of radii r1 and r2 in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to: (1) r1r2 (2) √r1r2 r1+r2 + r22 2 (3) √r21 (4) r1+r2

Q9. One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27°C to 37°C . If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? [R = 8. 314 J mol−1k−1] (1) work done by the gas is close to 332 J (2) work done on the gas is close to 582 J (3) work done by the gas is close to 582 J (4) work done on the gas is close to 332 J

Q9. A charge q is placed at one corner of a cube as shown in figure. The flux of electrostatic field E through the shaded area is: (1) q (2) q 8ε0 24ε0 (3) q (4) q 48ε0 4ε0

Q9. Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If the magnetic field at the center of A is 3 T the field at the center of C would be : (Assume that the magnetic field is confined with in the volume of respective solenoid). (1) 12 T (2) 6 T (3) 9 T (4) 1 T

Q9. A refrigerator consumes an average 35 W power to operate between temperature −10°C to 25°C. If there is no loss of energy then how much average heat per second does it transfer? (1) 350 J s−1 (2) 298 J s−1 (3) 263 J s−1 (4) 35 J s−1

Q9. A large number of water drops, each of radius r, combine to have a drop of radius R. If the surface tension is T and mechanical equivalent of heat is J , the rise in heat energy per unit volume will be: (1) 2TrJ (2) 3TrJ (3) 2TJ ( 1r −1R ) (4) 3TJ ( 1r −1R )

Q9. The length of a metal wire is ℓ1, when the tension in it is T1 and is ℓ2 when the tension is T2. The natural length of the wire is: JEE Main 2021 (20 Jul Shift 2) JEE Main Previous Year Paper (1) √ℓ1ℓ2 (2) ℓ1 TT2−ℓ22−T1T 1 (3) ℓ1 T 2+ℓ2 T 1 (4) ℓ1+ℓ2 T 2+T1 2

Q9. A polyatomic ideal gas has 24 vibrational modes. What is the value of γ? (1) 1. 03 (2) 1. 30 (3) 1. 37 (4) 10. 3

Q9. The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure. The potential energy U(x) versus time (t) plot of the particle is correctly shown in figure: (1) (2) (3) (4)

Q9. A block of mass 1 kg attached to a spring is made to oscillate with an initial amplitude of 12 cm . After 2 minutes the amplitude decreases to 6 cm . Determine the value of the damping constant for this motion. (take ln 2 = 0. 693 ) (1) 1. 16 × 10−2 kg s−1 (2) 3. 3 × 102 kg s−1 (3) 1. 16 × 102 kg s−1 (4) 5. 7 × 10−3 kg s−1

Q10.In the given figure, the emf of the cell is 2. 2 V and if internal resistance is 0. 6 Ω . Calculate the power dissipated in the whole circuit: JEE Main 2021 (26 Aug Shift 1) JEE Main Previous Year Paper (1) 1.32 W (2) 4 .4 W (3) 0. 65 W (4) 2. 2 W

Q10.A uniformly charged disc of radius R having surface charge density σ is placed in the xy plane with its center at the origin. Find the electric field intensity along the z-axis at a distance Z from origin: (1) 2ε0 1 (2) σ Z + + E = E = σ 2ε0 ( (Z 2+R2)1/2 (1 Z) (Z 2+R2)1/2 ) σ Z (3) σ 1 1 E = − E = 2ε0 ( (Z 2+R2) + Z 2 ) 2ε0 (Z 2+R2)1/2 ) (4) (1