Practice Questions

Q8. For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where γ is the ratio of specific heats): (1) −γ dVV (2) −γ dVV (3) −1γ dVV (4) dVV

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. The amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500 g , Decay constant = 20 g s−1 then how much time is required for the amplitude of the system to drop to half of its initial value? (ln 2 = 0. 693) (1) 34. 65 s (2) 17. 32 s (3) 0. 034 s (4) 15. 1 s

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 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. 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. 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. When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is: (1) straight line (2) elliptical (3) circular (4) parabolic

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 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. T0 is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to 161 times of its initial value, the modified time period is (1) T0 (2) 8πT0 (3) 4T0 (4) 14 T0

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. Consider a binary star system of star A and star B with masses mA and mB revolving in a circular orbit of radii rA and rB, respectively. If TA and TB are the time period of star A and star B, respectively, then: (1) TA rA 23 (2) TA = TB = TB ( rB ) (3) TA > TB (if mA > mB ) (4) TA > TB (if rA > rB )

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. 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. Each side of a box made of metal sheet in cubic shape is 𝑎 at room temperature 𝑇, the coefficient of linear expansion of the metal sheet is 𝛼. The metal sheet is heated uniformly, by a small temperature 𝛥𝑇, so that its new temperature is 𝑇+ 𝛥𝑇. Calculate the increase in the volume of the metal box. (1) 4𝑎3𝛼𝛥𝑇 (2) 3𝑎3𝛼𝛥𝑇 (3) 4𝜋𝑎3𝛼𝛥𝑇 (4) 43𝜋𝑎3𝛼𝛥𝑇

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 solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner → radius a and outer radius b as shown in the figure. The approximate variation electric field E , as a function of distance r , from centre O , is given by: (1) (2) (3) (4)

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. 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. The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T . Consider R as universal gas constant. The pressure of the mixture of gases is : (1) 88RT (2) 3RT V V (3) 5 RT (4) 4RT 2 V V

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. Which of the following equations represents a travelling wave? (1) y = A sin(15x −2t) (2) y =Aex cos(ωt −θ) (3) y = Ae−x2(vt + θ) (4) y = A sin x cos ωt