Practice Questions

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.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.When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is x , where x =_________. 8

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 ________

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 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 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 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 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 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.

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.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.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.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.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.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.A capacitor of 10μF capacitance whose plates are separated by 10 mm through air and each plate has area 4 cm2 is now filled equally with two dielectric media of K1 = 2, K2 = 3 respectively as shown in figure. If new force between the plates is 8 N . The supply voltage is _________ ×10−4 V . (we modified language of question to make it correct)

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.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.An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density +σ. The electron at t = 0 is at a distance of 1 m from S and has a speed of 1 m s−1 . The maximum value of σ, if the electron strikes S at t = 1 s is α[ mϵ0e ] m2C . The value of α is _____.

Q25.An electric field, E = √6 passes through the surface of 4 m2 area having unit vector ^n = ( √6 ) electric flux for that surface is ______ Vm .

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 )