Practice Questions

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. Which one is the correct option for the two different thermodynamic processes ? JEE Main 2021 (17 Mar Shift 2) JEE Main Previous Year Paper (1) (c) and (a) (2) (c) and (d) (3) (a) only (4) (b) and (c)

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. 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. The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9. 0 × 103 km. Find the mass of Mars. { Given 4π2G = 6 × 1011 N−1 m−2 kg2} (1) 5. 96 × 1019 kg (2) 3. 25 × 1021 kg (3) 7. 02 × 1025 kg (4) 6. 00 × 1023 kg

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. 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. 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. 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. 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. 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. 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

Q8. The length of metallic wire is l1 when tension in it is T1 . It is l2 when the tension is T2 . The original length of the wire will be : (1) T2l1+T1l2 (2) l1+l2 T1+T2 2 (3) T2l1−T1l2 (4) T1l1−T2l2 T2−T1 T2−T1

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. 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. A monoatomic ideal gas, initially at temperature 𝑇1 is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature 𝑇2 by releasing the piston suddenly. If 𝑙1 and 𝑙2 are 𝑇1 the lengths of the gas column, before and after the expansion respectively, then the value of will be: 𝑇2 (1) 𝑙1 23 (2) 𝑙2 23 𝑙2 𝑙1 (3) 𝑙2 (4) 𝑙1 𝑙1 𝑙2

Q8. A heat engine has an efficiency of 1 . When the temperature of sink is reduced by 62°C, its efficiency get 6 doubled. The temperature of the source is : (1) 124°C (2) 37°C (3) 62°C (4) 99°C JEE Main 2021 (25 Jul Shift 2) 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 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. 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. 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

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 →

Q8. A glass tumbler having inner depth of 17 . 5 cm is kept on a table. A student starts pouring water 𝜇= 4 into it 3 while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled ? (1) 10 cm (2) 11 . 7 cm (3) 7 . 5 cm (4) 8 . 75 cm JEE Main 2021 (01 Sep Shift 2) JEE Main Previous Year Paper

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