Practice Questions

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.Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total surface energy before and after the change is (1) 2 13 : 1 (2) 1 : 2 31 (3) 2 : 1 (4) 1 : 2

Q10.Two particles A and B having charges 20 μC and −5 μC respectively are held fixed with a separation of 5 cm At what position a third charged particle should be placed so that it does not experience a net electric force ? (1) At 5 cm from −5 μC on the right side (2) At 5 cm from 20 μC on the left side of system (3) At 1. 25 cm from −5 μC between two charges (4) At midpoint between two charges

Q10.A certain charge Q is divided into two parts q and (Q −q). How should the charges Q and q be divided so that q and (Q −q) placed at a certain distance apart experience maximum electrostatic repulsion? (1) Q = 2q (2) Q = 2q (3) Q = 4q (4) Q = 3q JEE Main 2021 (20 Jul Shift 1) JEE Main Previous Year Paper

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

Q10.A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire. (1) Loop assumes circular shape with its plane normal to the field. (2) Loop assumes circular shape with its plane parallel to the field. (3) Wire gets stretched to become straight. (4) Shape of the loop remains unchanged.

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

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 electrons each are fixed at a distance 2d. A third charge proton placed at the midpoint is displaced slightly by a distance x(x ≪d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency: ( m = mass of charged particle) (1) πε0md3 12 (2) 2πε0md3 12 ( 2q2 ) ( q2 ) 2 (3) 1 1 ( 2πε0md3q2 ) 2 (4) ( πε0md32q2 )

Q10.Figure shows a rod AB , which is bent in a 120° circular arc of radius R. A charge (−Q) is uniformly → distributed over rod AB. What is the electric filed E at the centre of curvature O ? (1) 3√3Q ˆi (2) 3√3Q ˆi 8π2ε0R2 8πε0R2 (3) −3√3Q ˆi (4) 3√3Q ˆi 8π2ε0R2 16π2ε0R2

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.Two ideal polyatomic gases at temperatures T1 and T2 are mixed so that there is no loss of energy. If F1 and F2, m1 and m2, n1 and n2 be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is: (1) n1 T 1+n2 T 2 (2) n1F1T1+n2F2T2 n1+n2 n1F1+n2F2 (3) n1 F 1 T 1+n2 F 2 T 2 (4) n1 F 1 T 1+n2 F 2 T 2 F 1+F2 n1+n2

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 parallel plate capacitor with plate area '𝐴' and distance of separation '𝑑' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as: 𝜀𝑥= 𝜀0 + 𝑘𝑥, for 0 < 𝑥≤ 𝑑2 ≤𝑥≤𝑑 𝜀𝑥= 𝜀0 + 𝑘𝑑- 𝑥, for 𝑑2 𝑘𝑑 (1) 2 / 𝑘𝐴 𝑘𝐴 (2) 𝜀0 + 2𝑙𝑛2𝜀0 + 𝑘𝑑 2 2𝜀0 (3) 0 (4) 𝑘𝐴 ln 2𝜀0 2 2𝜀0 - 𝑘𝑑

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 bob of mass 𝑚 suspended by a thread of length ℓ undergoes simple harmonic oscillations with time period 1 𝑇. If the bob is immersed in a liquid that has density times that of the bob and the length of the thread is 4 1 𝑟𝑑 increased by of the original length, then the time period of the simple harmonic oscillations will be: 3 3 4 (1) 4𝑇 (2) 3𝑇 (3) 𝑇 (4) 3 2𝑇

Q10.A Copper (Cu) rod of length 25 cm and cross-sectional area 3 mm2 is joined with a similar Aluminium (Al) rod as shown in figure. Find the resistance of the combination between the ends A and B. (Take resistivity of Copper = 1. 7 × 10−8 Ωm , Resistivity of aluminium = 2. 6 × 10−8 Ωm ) (1) 2. 170 mΩ (2) 1. 420 mΩ (3) 0. 0858 mΩ (4) 0. 858 mΩ

Q10.A mass of 5 kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4 m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed ? (1) 4 m s-2 (2) 8 m s-2 (3) 5 m s-2 (4) 10 m s-2

Q10.Given below are two statements: Statement I: A second's pendulum has a time period of 1 second. Statement II: It takes precisely one second to move between the two extreme positions. In the light of the above statements, choose the correct answer from the options given below (1) Statement I is false but Statement II is true (2) Both Statement I and Statement II are true (3) Both Statement I and Statement II are False (4) Statement I is true but Statement II is false

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.In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position. (1) 1 (2) 3 2 4 (3) 1 (4) 1 3 4

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.A student is performing the experiment of the resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m s−1 . The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is: JEE Main 2021 (25 Feb Shift 1) JEE Main Previous Year Paper (1) 14. 8 cm (2) 18. 4 cm (3) 16. 6 cm (4) 13 cm

Q10.Two Carnot engines A and B operate in series such that engine A absorbs heat at T1 and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at T3 . When workdone in both the cases is equal, to value of T is : (1) 2 3 T1 + 23 T3 (2) 31 T1 + 32 T3 (3) 32 T1 + 31 T3 (4) 32 T1 + 31 T3

Q11.The function of time representing a simple harmonic motion with a period of π is : ω (1) sin(ωt) + cos(ωt) (2) cos(ωt) + cos(2ωt) + cos(3ωt) (3) sin2(ωt) (4) 3 cos( π4 −2ωt)