Practice Questions

Q7. Calculate the value of the mean free path (λ) for oxygen molecules at temperature 27°C and pressure 1. 01 × 105 Pa . Assume the molecular diameter 0. 3 nm and the gas is ideal. (k = 1. 38 × 10−23 J K−1) (1) 58 nm (2) 32 nm (3) 86 nm (4) 102 nm

Q7. Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If √8R is the distance between the centres of a ring (of mass m ) and a sphere (mass M ) where both have equal radius R JEE Main 2021 (26 Feb Shift 1) JEE Main Previous Year Paper (1) 2√2 GMm (2) √8 GmM 3 R2 9 R 1 GMm (3) R2 (4) √827 GmMR2 3√8

Q7. A uniform heavy rod of weight 10 kg m s−2, cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 × 1011 N m−2. Neglecting the lateral contraction, JEE Main 2021 (31 Aug Shift 1) JEE Main Previous Year Paper find the elongation of rod due to its own weight: (1) 5 × 10−10 m (2) 4 × 10−8 m (3) 5 × 10−8 m (4) 2 × 10−9 m

Q7. What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T? (1) 2 3 kBT (2) kBT (3) 2 3 kBT (4) 21 kBT

Q7. The R.M.S. speeds of the molecules of Hydrogen, Oxygen, and Carbon dioxide at the same temperature are vH, vO and vC respectively, then: (1) vC > vO > vH (2) vH = vO > vC (3) vH > vO > vC (4) vH = vO = vC

Q7. Two discs have moments of intertia I1 and I2 about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, ω1 and ω2 respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by: (1) I1I2 (ω1 −ω2)2 (2) (ω1−ω2)2 (I1+I2) 2(I1+I2) (3) I1I2 (ω1 −ω2)2 (4) (I1−I2)2ω1ω2 2(I1+I2) 2(I1+I2)

Q7. The point A moves with a uniform speed along the circumference of a circle of radius 0. 36 m and covers 30° in 0. 1 s. The perpendicular projection P from A on the diameter MN represents the simple harmonic motion of P . The restoration force per unit mass when P touches M will be : (1) 0. 49 N (2) 9. 87 N (3) 50 N (4) 100 N

Q7. Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is 24 π × 102 N m−2 . What is the minimum radius of the wire ? ( take g = 10 m s−2) (1) 1250 cm (2) 1. 25 cm (3) 125 cm (4) 12. 5 cm

Q7. Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 × 103 kg . The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, JEE Main 2021 (31 Aug Shift 2) JEE Main Previous Year Paper calculate the compression strain of each column. [use 𝑌= 2 . 0 × 1011 Pa, 𝑔= 9 . 8 m s-2] (1) 1 . 87 × 10-3 (2) 2 . 60 × 10-7 (3) 3 . 60 × 10-8 (4) 7 . 07 × 10-4

Q7. An ideal gas is expanding such that PT 3 = constant. The coefficient of volume expansion of the gas is: (1) T2 (2) T3 (3) T1 (4) T4

Q7. A satellite is launched into a circular orbit of radius R around earth, while a second satellite is launched into a circular orbit of radius 1. 02 R. The percentage difference in the time periods of the two satellites is: (1) 1. 5 (2) 2. 0 (3) 0. 7 (4) 3. 0

Q7. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R . Assertion A : When a rod lying freely is heated, no thermal stress is developed in it. Reason R : On heating, the length of the rod increases. In the light of the above statements, choose the correct answer from the options given below: (1) Both A and R are true and R is the correct (2) A is false but R is true explanation of A (3) Both A and R are true but R is NOT the correct (4) A is true but R is false explanation of A

Q7. A cord is wound round the circumference of wheel of radius r, The axis of the wheel is horizontal and the moment of inertia about it is I . A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance h, the square of angular velocity of wheel will be (1) 2mgh (2) 2mgh I+mr2 I+2mr2 (3) 2gh (4) I+mr22gh

Q7. In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant k, the frequency of oscillation of given body is: (1) 1 2k (2) 1 k sin α 2π √ Mg sin α 2π √ Mg (3) 1 k (4) 1 2π √ 2M 2π √2kM

Q7. In thermodynamics, heat and work are : (1) Path functions (2) Intensive thermodynamic state variables (3) Extensive thermodynamic state variables (4) Point functions

Q7. Four particles each of mass 𝑀, move along a circle of radius 𝑅 under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is : (1) 1 𝐺𝑀 + 1 (2) 1 𝐺𝑀 2√ 𝑅2√2 2√ 𝑅( 2√2 + 1 ) (3) 1 𝐺𝑀 - 1 (4) 𝐺𝑀 2√ 𝑅2√2 √ 𝑅

Q7. Two different metal bodies 𝐴 and 𝐵 of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is: JEE Main 2021 (25 Jul Shift 1) JEE Main Previous Year Paper 8 3 (1) (2) 3 8 (3) 3 (4) 4 4 3

Q7. If 𝑌, 𝐾 and 𝜂 are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters. 9 𝐾𝜂 3𝑌𝐾 (1) 𝑌= m-2 (2) 𝜂= m-2 3 𝐾- 𝜂N 9𝐾+ 𝑌N (3) 𝐾= 𝑌𝜂 N m-2 (4) 𝑌= 9 𝐾𝜂 N m-2 9𝜂- 3𝑌 2𝜂+ 3 𝐾

Q7. What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T ? ( kB is Boltzmann constant) (1) 2 1 kBT (2) 32 kBT (3) 3 kBT (4) kBT 2

Q7. Two identical metal wires of thermal conductivities K1 and K2 respectively are connected in series. The effective thermal conductivity of the combination is: (1) 2 K1 K2 (2) K1+K2 K1+K2 2 K1 K2 (3) K1+K2 (4) K1 K2 K1 K2 K1+K2

Q7. The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is L. The magnitude of the areal velocity of the planet is : JEE Main 2021 (18 Mar Shift 2) JEE Main Previous Year Paper (1) 4L (2) L M M (3) 2L (4) L M 2M

Q7. The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from 0 °C to 50 °C when no work is done is (R is the universal gas constant) (1) 250R (2) 750R (3) 175R (4) 500R

Q8. A raindrop with radius R = 0. 2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is : [Density of water fw = 1000 kg m−3 and Density of air fa = 1. 2 kg m−3, g = 10 m/s2 Coefficient of viscosity of air = 1. 8 × 10−5N s m−2] (1) 250. 6 m s−1 (2) 43. 56 m s−1 (3) 4. 94 m s−1 (4) 14. 4 m s−1

Q8. In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A →B and C →D are T1 and T2( T 1 > T2) respectively. JEE Main 2021 (27 Jul Shift 1) JEE Main Previous Year Paper Choose the correct option out of the following for work done if processes BC and DA are adiabatic. (1) WAB = WDC (2) WAD = WBC (3) WBC + WDA > 0 (4) WAB < WCD

Q8. If one mole of the polyatomic gas is having two vibrational modes and β is the ratio of molar specific heats for polyatomic gas (β = CPCv ) then the value of β is : (1) 1. 02 (2) 1. 2 (3) 1. 25 (4) 1. 35