Practice Questions

Q9. A wire of length L is hanging from a fixed support. The length changes to L1 and L2 when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to (1) √L1 L2 (2) L1+L22 (3) 2L1 −L2 (4) 3L1 −L2

Q9. Two cells of the same EMF 𝐸 but different internal resistances 𝑟1 and 𝑟2 are connected in series with an external resistance 𝑅 as shown in the figure. The terminal potential difference across, the second cell is found to be zero. The external resistance 𝑅 must then be: (1) 𝑟1𝑟2 (2) 𝑟1 - 𝑟2 (3) 𝑟2 - 𝑟1 (4) 𝑟1 + 𝑟2

Q9. Sixty four conducting drops each of radius 0. 02 m and each carrying a charge of 5 μC are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be (1) 1 : 4 (2) 4 : 1 (3) 1 : 8 (4) 8 : 1

Q9. The root mean square speed of smoke particles of mass 5 × 10-17 kg in their Brownian motion in air at NTP is approximately. [Given 𝑘= 1 . 38 × 10-23J K-1] (1) 60 mm s-1 (2) 12 mm s-1 (3) 15 mm s-1 (4) 36 mm s-1

Q9. A teacher in his physics laboratory allotted an experiment to determine the resistance 𝐺 a galvanometer. 1 Students took the observations for deflection in the galvanometer. Which of the below is true for measuring 3 value of 𝐺? (1) 1 deflection method cannot be used for (2) 1 deflection method can be used and in this case 3 3 determining the resistance of the galvanometer. the 𝐺 equals to twice the value of shunt resistance(s). 1 1 (3) deflection method can be used and in this case, (4) deflection method can be used and in this case 3 3 the G equals to three times the value of shunt the 𝐺 value equals to the shunt resistance(s) resistance(s).

Q9. In the wave equation 𝑦= 0 . 5sin 𝜆400𝑡- 𝑥𝑚 the velocity of the wave will be : (1) 200 m s-1 (2) 200√2 m s-1 (3) 400 m s-1 (4) 400√2 m s-1

Q10.The total charge on the system of capacitance C1 = 1μF, C2 = 2μF, C3 = 4μF and C4 = 3μF connected in parallel is (Assume a battery of 20 V is connected to the combination) (1) 200μC (2) 200C (3) 10μC (4) 10C

Q10.A charge of 4μC is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be: (1) 1μC and 3μC (2) 2μC and 2μC (3) 0 and 4μC (4) 1. 5μC and 2. 5μC

Q10.A slab of dielectric constant K has the same crosssectional area as the plates of a parallel plate capacitor and thickness 3 d, where d is the separation of the plates. The capacitance of the capacitor when the slab is inserted 4 JEE Main 2022 (28 Jul Shift 2) JEE Main Previous Year Paper between the plates will be : (Given C0 = capacitance of capacitor with air as medium between plates.) (1) 4KC0 (2) 3KC0 3+K 3+K (3) 3+K (4) K 4KC0 4+K

Q10.A cylinder of fixed capacity of 44. 8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20. 0°C will be (Given gas constant R = 8. 3 J K−1 mol−1 ) (1) 249 J (2) 415 J (3) 498 J (4) 830 J

Q10.The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is (1) 12 s (2) 8 s (3) 36 s (4) 6 s

Q10.The equations of two waves are given by : y1 = 5 sin 2π(x −vt) cm y2 = 3 sin 2π(x −vt + 1. 5) cm These waves are simultaneously passing through a string. The amplitude of the resulting wave is : (1) 2 cm (2) 4 cm (3) 5. 8 cm (4) 8 cm

Q10.The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination α, is given by : (1) 2π√ (g cosL α) (2) 2π√ (g sinL α) (3) 2π√Lg (4) 2π√ (g tanL α)

Q10.What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen? (1) The velocity of atomic oxygen remains same (2) The velocity of atomic oxygen doubles (3) The velocity of atomic oxygen becomes half (4) The velocity of atomic oxygen becomes four times

Q10.Two uniformly charged spherical conductors 𝐴 and 𝐵 of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere 𝐴 and 𝐵 will be (1) 1: 2 (2) 2: 1 (3) 1: 1 (4) 1: 4

Q10.If 𝑛 represents the actual number of deflections in a converted galvanometer of resistance 𝐺 and shunt resistance 𝑆. Then the total current 𝐼 when its figure of merit is 𝐾 will be (1) 𝐾𝑆 (2) 𝐺+ 𝑆 𝑆+ 𝐺 𝑛𝐾𝑆 𝑛𝐾𝑆 𝑛𝐾𝐺+ 𝑆 (3) (4) 𝐺+ 𝑆 𝑆

Q10.A long straight wire with a circular cross-section having radius 𝑅, is carrying a steady current 𝐼. The current 𝐼 is uniformly distributed across this cross-section. Then the variation of magnetic field due to current 𝐼 with distance 𝑟𝑟< 𝑅 from its centre will be (1) 𝐵∝𝑟 (2) 𝐵∝1 𝑟 1 (3) 𝐵∝𝑟2 (4) 𝐵∝ 𝑟2

Q10.Two capacitors, each having capacitance 40𝜇F are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant 𝐾 such that the equivalence capacitance of the system became 24𝜇F. The value of 𝐾 will be : (1) 1 . 5 (2) 2 . 5 (3) 1 . 2 (4) 3

Q10.According to kinetic theory of gases, A. The motion of the gas molecules freezes at 0°C. B. The mean free path of gas molecules decreases if the density of molecules is increased. C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant. D. Average kinetic energy per molecule per degree of freedom is 3 2 kBT (for monoatomic gases). Choose the most appropriate answer from the options given below (1) A and C only (2) B and C only (3) A and B only (4) C and D only

Q10.Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is √2 times the speed of sound, then the value of n will be (1) 1 (2) 2 (3) 3 (4) 4

Q10.The motion of a simple pendulum executing S.H.M. is represented by the following equation y = A sin(πt + ϕ), where time is measured in second. The length of pendulum is (1) 97. 23 cm (2) 25. 3 cm (3) 99. 4 cm (4) 406. 1 cm

Q10.Two identical positive charges Q each are fixed at a distance of 2a apart from each other. Another point charge q0 with mass m is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge q0 executes SHM. The time period of oscillation of charge q0 will be (1) √4π3ε0ma3q0Q (2) √ 4π3ε0ma3q0Q (3) √2π2ε0ma3q0Q (4) √8π3ε0ma3q0Q

Q10.Two capacitors having capacitance C1 and C2 respectively are connected as shown in figure. Initially, capacitor C1 is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor C1 is now connected to uncharged capacitor C2 by closing the switch S . The amount of charge on the capacitor C2 , after equilibrium, is JEE Main 2022 (26 Jun Shift 1) JEE Main Previous Year Paper (1) C1C2 V (2) (C1+C2) V (C1+C2) C1C2 (3) (C1 + C2)V (4) (C1 −C2)V

Q10.Two light beams of intensities in the ratio of 9 : 4 are allowed to interfere. The ratio of the intensity of maxima and minima will be : (1) 9 : 4 (2) 16 : 81 (3) 25 : 169 (4) 25 : 1

Q10.The charge on capacitor of capacitance 15μF in the figure given below is (1) 60 μC (2) 130 μC (3) 260 μC (4) 585 μC