Practice Questions

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

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. 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. 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

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

Q9. An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is S1 and that of the other part is S2 . Given that S1 > S2 . If the piston is removed then the total entropy of the system will be: (1) S1 × S2 (2) S1 −S2 (3) S1 (4) S1 + S2 S2

Q9. Match List I with List II . List I List II (a) Isothermal (i) Pressure constant (b) Isochoric (ii) Temperature constant (c) Adiabatic (iii) Volume constant (d) Isobaric (iv) Heat content is constant Choose the correct answer from the options given below: (1) ( a ) →( ii ) , ( b ) →( iii ) , ( c ) →( iv ) , ( d ) →( i ) (2) ( a ) →( iii ) , ( b ) →( ii ) , ( c ) →( i ) , ( d ) →( iv ) (3) ( a ) →( i ) , ( b ) →( iii ) , ( c ) →( ii ) , ( d ) →( iv ) (4) ( a ) →( ii ) , ( b ) →( iv ) , ( c ) →( iii ) , ( d ) →( i ) Q10.𝑛 mole of a perfect gas undergoes a cyclic process 𝐴𝐵𝐶𝐴 (see figure) consisting of the following processes. 𝐴→𝐵: Isothermal expansion at temperature 𝑇 so that the volume is doubled from 𝑉1 to 𝑉2 = 2𝑉1 and pressure changes from 𝑃1 to 𝑃2 𝐵→𝐶: Isobaric compression at pressure 𝑃2 to initial volume 𝑉1 . 𝐶→𝐴: Isochoric change leading to change of pressure from 𝑃2 to 𝑃1 Total work done in the complete cycle 𝐴𝐵𝐶𝐴 is: JEE Main 2021 (24 Feb Shift 1) JEE Main Previous Year Paper 1 (1) 𝑛𝑅𝑇ln2 - (2) 𝑛𝑅𝑇ln2 2 (3) 𝑛𝑅𝑇ln2 + 1 (4) 0 2

Q9. For a gas 𝐶P - 𝐶V = 𝑅 in a state 𝑃 and 𝐶P - 𝐶V = 1 . 10𝑅 in a state 𝑄, 𝑇P and 𝑇Q are the temperatures in two different states 𝑃 and 𝑄, respectively. Then (1) 𝑇P = 𝑇Q (2) 𝑇P < 𝑇Q (3) 𝑇P = 0 . 9𝑇Q (4) 𝑇P > 𝑇Q

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

Q9. If the time period of a two meter long simple pendulum is 2 s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is: (1) 2π2 m s−2 (2) 16 m s−2 (3) π2 m s−2 (4) 9. 8 m s−2

Q9. Consider a mixture of gas molecule of types A, B and C having masses mA < mB < mC. The ratio of their root mean square speeds at normal temperature and pressure is: (1) vA = vB = vC = 0 (2) 1 > 1 > 1 vA vB vC (3) vA = vB ≠vC (4) 1 < 1 < 1 vA vB vC

Q9. If the R.M.S. speed of oxygen molecules at 0°C is 160 m s−1 . Find the R.M.S. speed of hydrogen molecules at 0°C . (1) 40 m s−1 (2) 80 m s−1 (3) 640 m s−1 (4) 332 m s−1

Q9. Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g , the time period of pendulum will be : 2 (1) √3T (2) T √3 (3) (4) T T √32 √23

Q10.A resistor develops 500 J of thermal energy in 20 s when a current of 1. 5 A is passed through it. If the current is increased from 1. 5 A to 3 A , what will be the energy developed in 20 s. (1) 1500 J (2) 1000 J (3) 500 J (4) 2000 J → → →

Q10.Two particles A and B of equal masses are suspended from two massless springs of spring constants K1 and K2 respectively.If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is (1) K2 (2) K1 K1 K2 (3) √K1K2 (4) √K2K1

Q10.Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root-mean-square (RMS) velocity to the average velocity of the gas molecule would be : (Molecular weight of oxygen is 32 g mol−1; R = 8. 3 J K−1 mol−1 ) (1) √33 (2) √83 (3) √3π8 (4) √8π3

Q10.A particle starts executing simple harmonic motion (SHM) of amplitude a and total energy E. At any instant, its kinetic energy is 3E , then its displacement y is given by: 4 (1) y = a (2) y = a √2 (3) y = a√32 (4) y = a2

Q10.A cylindrical container of volume 4. 0 × 10−3 m3 contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K. The pressure of the mixture of gases is : [Take gas constant as 8. 3 J mol−1 K−1] (1) 24. 9 × 103 Pa (2) 249 × 101 Pa (3) 24. 9 × 105 Pa (4) 24. 9 Pa

Q10.In a ferromagnetic material, below the curie temperature, a domain is defined as: (1) a macroscopic region with saturation magnetization. (2) a macroscopic region with consecutive magnetic dipoles oriented in opposite direction. (3) a macroscopic region with zero magnetization. (4) a macroscopic region with randomly oriented magnetic dipoles. JEE Main 2021 (25 Feb Shift 2) JEE Main Previous Year Paper

Q10.The temperature θ at the junction of two insulating sheets, having thermal resistances R1 and R2 as well as top and bottom temperatures θ1 and θ2 (as shown in figure) is given by : (1) θ1R2−θ2R1 (2) θ2R2−θ1R1 R2−R1 R2−R1 (3) θ1R2+θ2R1 (4) θ1R1+θ2R2 R1+R2 R1+R2

Q10.A 25 m long antenna is mounted on an antenna tower. The height of the antenna tower is 75 m . The wavelength (in meter) of the signal transmitted by this antenna would be : (1) 300 (2) 400 (3) 200 (4) 100

Q11.For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal? JEE Main 2021 (17 Mar Shift 1) JEE Main Previous Year Paper (1) x = 0 (2) x = ±A (3) x = ± A (4) x = A2 √2

Q11.A charge Q is moving dl distance in the magnetic field B. Find the value of work done by B. (1) 1 (2) Infinite (3) Zero (4) −1 → x . A square loop of side d is placed with its edges along

Q11.Two ideal electric dipoles A and B, having their dipole moment p1 and p2 respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 37° with the axis. The ratio of the dipole moment of A and B, p1 is : ( take sin 37°= 53 ) p2 (1) 3 (2) 3 8 2 (3) 2 (4) 4 3 3

Q11. A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains: (1) have no relation with external magnetic field. (2) decrease in size and changes orientation. (3) increase in size but no change in orientation. (4) may increase or decrease in size and change its orientation.