Practice Questions

Q21.A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B = 0. 8 T . When released the radius of the loop starts shrinking at a constant rate of 2 cm s–1 . The induced emf in the loop at an instant when the radius of the loop is 10 cm will be ______ mV.

Q21.For the given figures, choose the correct options: (1) The rms current in circuit (b) can never be larger (2) The rms current in figure (a) is always equal to than that in (a) that in figure (b) (3) The rms current in circuit (b) can be larger than (4) At resonance, current in (b) is less than that in (a) that in (a)

Q21.For a moving coil galvanometer, the deflection in the coil is 0. 05 rad when a current of 10 mA is passed through it. If the torsional constant of suspension wire is 4. 0 × 10–5 N m rad−1 , the magnetic field is 0. 01 T and the number of turns in the coil is 200 , the area of each turn (in cm2 ) is : (1) 2. 0 (2) 1. 0 (3) 1. 5 (4) 0. 5

Q22.A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52 . 5 N. The angular acceleration of the cylinder will be _____ rad s-2.

Q22.A series combination of resistor of resistance 100 Ω inductor of inductance 1 H and capacitor of capacitance 6. 25 μF is connected to an ac source. The quality factor of the circuit will be _____.

Q22.A force 𝐹= 2 + 3𝑥 ^𝑖 acts on a particle in the 𝑥 direction where 𝐹 is in Newton and 𝑥 is in meter. The work done by this force during a displacement from 𝑥 = 0 to 𝑥= 4 m is _____ J.

Q22.A force of -𝑃 ^𝑘 acts on the origin of the coordinate system. The torque about the point ( 2, - 3 ) is 𝑃(𝑎 ^𝑖+ 𝑏 ^𝑗) 𝑎 𝑥 , The ratio of is The value of 𝑥 is 𝑏 2.

Q22.A series LCR circuit consists of R = 80 Ω. XL = 100 Ω , and XC = 40 Ω. The input voltage is 2500 cos(100πt) V. The amplitude of current, in the circuit, is _____ A .

Q22.A lift of mass 𝑀= 500 kg is descending with speed of 2 m s-1. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of 2 m s-2. The kinetic energy of the lift at the end of fall through to a distance of 6 m will be ______ kJ.

Q22.A square shaped coil of area 70 cm2 having 600 turns rotates in a magnetic field of 0. 4 Wb m–2 , about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil JEE Main 2023 (01 Feb Shift 2) JEE Main Previous Year Paper completes 500 revolution in a minute, the instantaneous emf when the plane of the coil is inclined at 60° with the field, will be ______ V. (Take π = 227 )

Q22.A thin uniform rod of length 2 m, cross sectional area 𝐴 and density 𝑑 is rotated about an axis passing through the centre and perpendicular to its length with angular velocity 𝜔. If value of 𝜔 in terms of its 𝛼𝐸 rotational kinetic energy 𝐸 is √ 𝐴𝑑, then the value of 𝛼 is ______.

Q22.Given below are two statements: Statement I : When the frequency of an AC source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases. Statement II : In a series LCR circuit, the value of power factor at resonance is one. In the light of given statements, choose the most appropriate answer from the options given below. (1) Statement I is incorrect but Statement II is true (2) Both Statement I and Statement II are false (3) Both Statement I and Statement II are true (4) Statement I is correct but Statement II is false

Q22.An LCR series circuit of capacitance 62. 5 nF and resistance of 50 Ω, is connected to an A.C. source of frequency 2. 0 kHz . For maximum value of amplitude of current in circuit, the value of inductance is ____ mH . (Take π2 = 10)

Q22.A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of 5th second. The force acted on the body is _____ N.

Q22.Which of the following Maxwell’s equation is valid for time varying conditions but not valid for static conditions: → → → → (1) (2) ∮ B ⋅ dl = μ0I ∮ E ⋅ dl = 0 −→ → → (3) ∮→D ⋅dA = Q (4) ∮ E ⋅dl = −∂ϕB∂t

Q22.A metallic cube of side 15 cm moving along y-axis at a uniform velocity of 2 m s−1 . In a region of uniform magnetic field of magnitude 0. 5 T directed along z- axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be mV.

Q22.A particle of mass 10 g moves in a straight line with retardation 2𝑥, where 𝑥 is the displacement in SI units. 10 -𝑛 Its loss of kinetic energy for above displacement is J . The value of 𝑛 will be ________ . 𝑥

Q22.Three identical resistors with resistance R = 12 Ω and two identical inductors with sell inductance L = 5 mH are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switch has been closed will be________ A. JEE Main 2023 (24 Jan Shift 2) JEE Main Previous Year Paper

Q22.The magnetic intensity at the centre of a long current carrying solenoid is found to be 1. 6 × 103 A m−1 . If the number of turns is 8 per cm, then the current flowing through the solenoid is ______A.

Q22.Two concentric circular coils with radii 1 cm and 1000 cm and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _____ ×10–8 H . (Take, π2 = 10 )

Q22.A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively (ksph : kcyl) is 2 : √x. The value of x is _______.

Q22.If the earth suddenly shrinks to 1 of its original volume with its mass remaining the same, the period of 64th 24 rotation of earth becomes 𝑥ℎ. The value of 𝑥 is ________

Q23.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : EM waves used for optical communication have longer wavelengths than that of microwave, employed in Radar technology. Reason R : Infrared EM waves are more energetic than microwaves, (used in Radar) In the light of given statements, choose the correct answer from the options given below. JEE Main 2023 (12 Apr Shift 1) JEE Main Previous Year Paper (1) Both A and R are true but R is NOT the correct (2) A is false but R is true explanation of A (3) A is true but R is false (4) Both A and R are true and R is the correct explanation of A

Q23.A solid sphere of mass 500 g radius 5 cm is rotated about one of its diameter with angular speed of 10 rad s-1. If the moment of inertia of the sphere about its tangent is 𝑥× 10-2 times its angular momentum about the diameter. Then the value of 𝑥 will be

Q23.A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is 7 × 10-3 J. The speed of the centre of mass of the sphere is ______ cm s-1.