Practice Questions

Q14.Choose the correct length (L) versus square of time period (T2) ) graph for a simple pendulum executing simple harmonic motion. JEE Main 2023 (01 Feb Shift 2) JEE Main Previous Year Paper (1) (2) (3) (4)

Q14.The displacement equations of two interfering waves are given by y1 = 10 sin (ωt + π3 ) cm, cm respectively. The amplitude of the resultant wave is _____ cm. y2 = 5[sin (ωt) + √3 cos ωt]

Q14.The free space inside a current carrying toroid is filled with a material of susceptibility 2 × 10-2. The percentage increase in the value of magnetic field inside the toroid will be (1) 0 . 2% (2) 0 . 1% (3) 2% (4) 1%

Q14.Given below are two statements: Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor. Statement II: An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non- zero power factor. In the light of above statements, choose the correct answer from the options given below: (1) Statement I is false but statement II is true (2) Statement I is true but statement II is false (3) Both Statement I and Statement II are false (4) Both Statement I and Statement II are true

Q14.A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental of 180 Hz will be _____ cm

Q14.A rod with circular cross-section area 2 cm2 and length 40 cm is wound uniformly with 400 turns of an insulated wire. If a current of 0 . 4 A flows in the wire windings, the total magnetic flux produced inside windings is 4π × 10-6 Wb. The relative permeability of the rod is (Given : Permeability of vacuum μ0 = 4π × 10-7 N A-2) 32 (1) 12 . 5 (2) 5 (3) 125 (4) 5 16

Q14.For the plane electromagnetic wave given by 𝐸= 𝐸0sin ( 𝜔𝑡– 𝑘𝑥) and 𝐵= 𝐵0sin ( 𝜔𝑡- 𝑘𝑥) , the ratio of average electric energy density to average magnetic energy density is 1 (1) (2) 2 2 (3) 4 (4) 1

Q14.A conducting loop of radius cm is placed perpendicular to a uniform magnetic field of 0 . 5 T. The √𝜋 magnetic field is decreased to zero in 0 . 5 s at a steady rate. The induced emf in the circular loop at 0 . 25 s is: (1) emf = 1mV (2) emf = 10mV (3) emf = 100mV (4) emf = 5mV

Q14.A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be (1) 1 : 1 (2) 1 : 3 (3) 2 : 1 (4) 1 : 4

Q14.The magnetic moments associated with two closely wound circular coils 𝐴 and 𝐵 of radius 𝑟𝐴= 10 cm and 𝑟𝐵= 20 cm respectively are equal if: (Where 𝑁𝐴, 𝐼𝐴 and 𝑁𝐵, 𝐼𝐵 are number of turn and current of 𝐴 and 𝐵 respectively) (1) 2𝑁𝐴𝐼𝐴= 𝑁𝐵𝐼𝐵 (2) 𝑁𝐴= 2𝑁𝐵 (3) 𝑁𝐴𝐼𝐴= 4𝑁𝐵𝐼𝐵 (4) 4𝑁𝐴𝐼𝐴= 𝑁𝐵𝐼𝐵

Q14.At a given point of time the value of displacement of a simple harmonic oscillator is given as y = A cos(30°). If amplitude is 40 cm and kinetic energy at that time is 200 J, the value of force constant 1. 0 × 10x N m–1 . The value of x is _____.

Q14.In the given circuit, the current I through the battery will be (1) 2. 5 A (2) 1 A (3) 2 A (4) 1. 5 A

Q14.Match the List-I with List-II. List I List II A AC generator I Presence of both L and C B Transformer II Electromagnetic Induction C Resonance phenomenon to occur III Quality factor D Sharpness of resonance IV Mutual Inductance Choose the correct answer from the options given below: (1) A-IV, B-II, C-I, D-III (2) A-II, B-I, C-III, D-IV (3) A-II, B-IV, C-I, D-III (4) A-IV, B-III, C-I, D-II

Q14.The distance between two consecutive points with phase difference of 60° in a wave of frequency 500 Hz is 6. 0 m . The velocity with which wave is travelling is ______ km s−1 .

Q15.An organ pipe 40 cm long is open at both ends. The speed of sound in air is 360 m s−1 . The frequency of the second harmonic is _ ________ Hz.

Q15.As shown in the figure, a point charge Q is placed at the centre of conducting spherical shell of inner radius a and outer radius b. The electric field due to charge Q in three different regions I, II and III is given by : (I : r < a, II : a < r < b, III : r > b) (1) EI = 0, EII = 0, EIII ≠0 (2) EI ≠0, EII = 0, EIII ≠0 (3) EI ≠0, EII = 0, EIII = 0 (4) EI = 0, EII = 0, EIII = 0

Q15.A cubical volume is bounded by the surfaces x = 0, x = a, y = 0, y = a, z = 0, z = a . The electric field in → the region is given by E = E0xˆi. Where E0 = 4 × 104 NC−1 m−1 . If a = 2 cm , the charge contained in the cubical volume is Q × 10–14 C . The value of Q is ______. (Take ϵ0 = 9 × 10−12 C2 N−1m−2 )

Q15.Given below are two statements: Statement I: Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an 𝐴𝐶 source, when resonance occurs. Statement II: Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage. In the light of the above statements, choose the correct answer from the options given below: (1) Statement I is false but Statement II is true (2) Both Statement I and Statement II are true (3) Statement I is true but Statement II is false (4) Both Statement I and Statement II are false

Q15.In a cuboid of dimension 2L × 2L × L , a charge q is placed at the centre of the surface S having area of 4L2 . The flux through the opposite surface to S is given by (1) q (2) q 12∈0 3∈0 (3) q (4) q 2∈0 6∈0

Q15.If V is the gravitational potential due to sphere of uniform density on its surface, then its value at the centre of sphere will be: (1) 4 V (2) V 3 2 (3) V (4) 3V 2

Q15.A point charge 2 × 10–2 C is moved from P to S in a uniform electric field of 30 N C–1 directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be (1) 1200 mJ (2) 600 mJ (3) −600 mJ (4) −1200 mJ

Q15.A uniform electric field of 10 N C−1 is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0. 5 eV. The length of each plate is 10 cm. The angle (θ) of deviation of the path of electron as it comes out of the field is ______(in degree). JEE Main 2023 (25 Jan Shift 1) JEE Main Previous Year Paper

Q15.The ratio of intensities at two points P and Q on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are π and π respectively are 3 2, (1) 2 : 3 (2) 1 : 3 (3) 3 : 1 (4) 3 : 2

Q15.The electric potential at the centre of two concentric half rings of radii R1 and R2 , having same linear charge density λ is . (1) 2λ (2) λ ∈0 2∈0 (3) λ (4) λ 4∈0 ∈0

Q15.For a certain organ pipe, the first three resonance frequencies are in the ratio of 1 : 3 : 5 respectively. If the frequency of fifth harmonic is 405 Hz and the speed of sound in air is 324 m s–1 the length of the organ pipe is _____ m .