Practice Questions

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 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.Statement-I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive. Statement-II : An electric dipole is placed in a uniform electric field. The net electric force on the dipole will not be zero. (1) Both statement-I and statement-II are true. (2) Both statement-I and statement-II are false. (3) Statement-I is true but statement-II is false. (4) Statement-I is false but statement-II is true.

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.A condenser of 2 𝜇F capacitance is charged steadily from 0 to 5 C. Which of the following graph represents correctly the variation of potential difference𝑉 across its plates with respect to the charge 𝑄 on the condenser? (1) (2) (3) (4)

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 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.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.Two identical metallic spheres 𝐴 and 𝐵 when placed at certain distance in air repel each other with a force of 𝐹 . Another identical uncharged sphere 𝐶 is first placed in contact with 𝐴 and then in contact with 𝐵 and finally placed at midpoint between spheres 𝐴and 𝐵. The force experienced by sphere 𝐶 will be : 3𝐹 3𝐹 (1) (2) 2 4 (3) 𝐹 (4) 2𝐹

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.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

Q11.A parallel plate capacitor with plate area A and plate separation d = 2 m has a capacitance of 4 μF. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant K = 3 (as shown in figure) will be JEE Main 2022 (26 Jun Shift 2) JEE Main Previous Year Paper (1) 2 μF (2) 32 μF (3) 6 μF (4) 8 μF

Q11.The current I in the given circuit will be (1) 10A (2) 20A (3) 4A (4) 40A + T. If it has an acceleration of

Q11.A wire of resistance 𝑅1$R_{1}$ is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is: (1) 9: 1 (2) 1: 9 (3) 4: 1 (4) 3: 1

Q11.Given below are two statements : Statement - I : Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature. Statement - II : Diamagnetism is a result of orbital motions of electrons developing magnetic moments opposite to the applied magnetic field. Choose the correct answer from the options given below (1) Both Statement - I and Statement - II are true. (2) Both Statement - I and Statement - II are false. (3) Statement - I is true but Statement - II is false. (4) Statement- I is false but Statement - II is true.

Q11.The equation of a particle executing simple harmonic motion is given by x = sin π(t + 13 ) m. At t = 1 s, the speed of particle will be (Given: π = 3. 14) (1) 157 cm s−1 (2) 0 cm s−1 (3) 272 cm s−1 (4) 314 cm s−1

Q11.Two identical charged particles each having a mass 10 g and charge 2. 0 × 10−7C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0. 25, find the value of L. [Use g = 10 ms−2 ] (1) 12 cm (2) 10 cm (3) 8 cm (4) 5 cm

Q11.Capacitance of an isolated conducting sphere of radius R1 becomes n times when it is enclosed by a concentric conducting sphere of radius R2 connected to earth. The ratio of their radii ( R2R1 ) is: (1) n (2) 2n n−1 2n+1 (3) n+1 (4) 2n+1 n n

Q11.Two point charges A and B of magnitude +8 × 10−6C and −8 × 10−6C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6. 4 × 104 N C−1 . The distance ' d' between the point charges A and B is (1) 2 m (2) 3 m (3) 1 m (4) 4 m

Q11.Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-point on the perpendicular bisector. The value of x at which charge q will experience the maximum Coulomb's force is: (1) d (2) d 2 (3) d (4) d √2 2√2

Q11.A longitudinal wave is represented by y = 10 sin 2π(nt −xλ ) cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to (1) 2π (2) 5π (3) π (4) 5π 2

Q11.A source of potential difference 𝑉 is connected to the combination of two identical capacitors as shown in the figure. When key 𝐾 is closed, the total energy stored across the combination is 𝐸1. Now key 𝐾 is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored 𝐸1 across the combination is now 𝐸2. The ratio will be 𝐸2 1 2 (1) (2) 10 5 5 5 (3) (4) 13 26

Q11.A. The drift velocity of electrons decreases with the increase in the temperature of conductor. B. The drift velocity is inversely proportional to the area of cross-section of given conductor. C. The drift velocity does not depend on the applied potential difference to the conductor. D. The drift velocity of electron is inversely proportional to the length of the conductor. E. The drift velocity increases with the increase in the temperature of conductor. Choose the correct answer from the options given below: (1) A and B only (2) A and D only (3) B and E only (4) B and C only

Q11.An observer moves towards a stationary source of sound with a velocity one-fifth of the velocity of sound. The percentage change in the apparent frequency is (1) zero (2) 5% (3) 10% (4) 20%