Practice Questions

Q24.A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4 m, then the time period of small oscillations will be _________s. [take 𝑔= 𝜋2 m s-2]

Q24.A particle executes simple harmonic motion with an amplitude of 4 cm . At the mean position, velocity of the particle is 10 cm s−1 . The distance of the particle from the mean position when its speed becomes 5 cm s−1 is √α cm , where α =______. JEE Main 2024 (27 Jan Shift 1) JEE Main Previous Year Paper

Q24.An object of mass 0.2 kg executes simple harmonic motion along x axis with frequency of ( 25π )Hz. At the position x = 0.04 m the object has kinetic energy 0.5 J and potential energy 0.4 J. The amplitude of oscillation is _____ cm .

Q24.Three capacitors of capacitances 25μF, 30μF and 45μF are connected in parallel to a supply of 100 V . Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is 9 E . The value of x is _____. x

Q24.A soap bubble is blown to a diameter of 7 cm.36960erg of work is done in blowing it further. If surface tension of soap solution is 40dyne/cm then the new radius is______ cm Take (π = 227 )

Q24.A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is ( a−1a ) then the value of a is ________ → 2^i+6^j+8^k 2^i+^j+^k . The

Q24.A particle performs simple harmonic motion with amplitude 𝐴. Its speed is increased to three times at an 2𝐴 𝑛𝐴 instant when its displacement is . The new amplitude of motion is . The value of 𝑛 is _____. 3 3

Q24.A tuning fork resonates with a sonometer wire of length 1 m stretched with a tension of 6 N . When the tension in the wire is changed to 54 N, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is _______ Hz .

Q24.Two open organ pipes of lengths 60 cm and 90 cm resonate at 6th and 5th harmonics respectively. The difference of frequencies for the given modes is _______ Hz . (Velocity of sound in air = 333 m/s )

Q24.The time period of simple harmonic motion of mass 𝑀 in the given figure is 𝜋√ 𝛼𝑀5𝐾, where the value of _______. JEE Main 2024 (31 Jan Shift 2) JEE Main Previous Year Paper

Q24.In a closed organ pipe, the frequency of fundamental note is 30 Hz. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to 110 Hz. If the organ pipe has a cross- sectional area of 2 cm2 , the amount of water poured in the organ tube is ________ g. (Take speed of sound in air is 330 m s−1 )

Q25.Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point P is xσ . The value of x is _______ (all quantities are measured in SI units). ϵo JEE Main 2024 (06 Apr Shift 1) JEE Main Previous Year Paper

Q25.A particle of mass 0.50 kg executes simple harmonic motion under force F = −50 (Nm−1)x. The time period of oscillation is 35 x s. The value of x is _______ (Given π = 227 )

Q25.In the given circuit, the current flowing through the resistance 20 Ω is 0. 3 A, while the ammeter reads 0. 9 A. The value of R1 is _____ Ω .

Q25.The electric field between the two parallel plates of a capacitor of 1.5μF capacitance drops to one third of its initial value in 6.6μs when the plates are connected by a thin wire. The resistance of this wire is _____ Ω . (Given, log 3 = 1.1 )

Q25.A parallel plate capacitor with plate separation 5 mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 mm, while keeping the battery connections intact, the capacitor draws 25% more charge from the battery than before. The dielectric constant of the sheet is ____.

Q25.Suppose a uniformly charged wall provides a uniform electric field of 2 × 104 N C-1 normally. A charged particle of mass 2 g being suspended through a silk thread of length 20 cm and remain stayed at a distance 1 of 10 cm from the wall. Then the charge on the particle will be 𝜇C where 𝑥= ________ [use √x 𝑔= 10 m s-2]

Q25.At the centre of a half ring of radius R = 10 cm and linear charge density 4nCm−1 , the potential is xπV . The value of x is _______ JEE Main 2024 (09 Apr Shift 1) JEE Main Previous Year Paper

Q25.If the net electric field at point P along Y axis is zero, then the ratio of q2 is 8 , where x = _____. q3 5√x

Q25.The distance between charges +𝑞 and -𝑞 is 2𝑙 and between +2𝑞 and -2𝑞 is 4𝑙. The electrostatic potential at point 𝑃 at a distance 𝑟 from centre 𝑂 is -𝛼𝑞𝑙 × 109 V, where the value of 𝛼 is ______. (Use 𝑟2 1 = 9 × 109 N m2 C-2) 4𝜋𝜀0 2

Q25.The electric field at point p due to an electric dipole is E. The electric field at point R on equitorial line will be E . The value of x : x

Q25.A parallel plate capacitor of capacitance 12.5pF is charged by a battery connected between its plates to potential difference of 12.0 V. The battery is now disconnected and a dielectric slab (ϵr = 6) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is _____ 10−12 J.

Q25.A capacitor of capacitance C and potential V has energy E. It is connected to another capacitor of capacitance 2C and potential 2V . Then the loss of energy is x3 E , where x is _______.

Q25.Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle 𝜃 with each other. When suspended in water the angle remains the same. If density of the material of the sphere is 1 . 5 g / cc, the dielectric constant of water will be ______. (Take density of water = 1 g / cc)

Q25.An infinite plane sheet of charge having uniform surface charge density +σsC/m2 is placed on x −y plane. Another infinitely long line charge having uniform linear charge density +λeC/m is placed at z = 4 m plane and parallel to y-axis. If the magnitude values |σs| = 2 |λe| then at point (0, 0, 2), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is π√n : 1. The value of n is_______.