Practice Questions

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.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.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 particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s. The maximum velocity of the particle is _______ cm/s.

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.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.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 )

Q24.A simple harmonic oscillator has an amplitude A and time period 6π second. Assuming the oscillation starts from its mean position, the time required by it to travel from x = A to x = √32 A will be πx s, where x = _______.

Q24.A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tension _____ cm .

Q24.The displacement of a particle executing SHM is given by x = 10 sin (wt + π3 )m. The time period of motion is 3.14 s. The velocity of the particle at t = 0 is ______ m/s.

Q24.A mass 𝑚 is suspended from a spring of negligible mass and the system oscillates with a frequency 𝑓1 . The frequency of oscillations if a mass 9𝑚 is suspended from the same spring is 𝑓2 . The value of 𝑓1 is _____ . 𝑓2

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.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.At room temperature (27∘C), the resistance of a heating element is 50Ω. The temperature coefficient of the material is 2.4 × 10−4∘C−1 . The temperature of the element, when its resistance is 62Ω, is _____ ∘C.

Q24.A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm, both vibrating in fundamental mode. The velocity of sound is ______ m s-1.

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.The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of 4 m, 2 ms−1 and 16 ms−2 at a certain instant. The amplitude of the motion is √x, m where x is ________

Q25.A thin metallic wire having cross sectional area of 10−4 m2 is used to make a ring of radius 30 cm. A positive charge of 2π C is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the centre of the ring. The tension in the ring is _______ N; provided that the ring does not get deformed (neglect the influence of gravity). (Given, 1 = 9 × 109 SI units) 4πϵ0

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_______.

Q25.A point source is emitting sound waves of intensity 16 × 10-8 W m-2 at the origin. The difference in intensity (magnitude only) at two points located at a distances of 2 m and 4 m from the origin respectively will be ________ × 10-8 W m-2.

Q25.The electric potential at the surface of an atomic nucleus ( 𝑍= 50 ) of radius 9 × 10-13 cm is 𝛼× 106 V. What is the value of 𝛼? (Charge of proton 1 . 6 × 10-19 C)

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.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.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 )