Practice Questions

Q21.In the given figure, an inductor and resistor are connected in series with a battery of emf E volt. Ea2b J s−1 represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of b will be _____. a JEE Main 2023 (13 Apr Shift 1) JEE Main Previous Year Paper

Q21.A closed circular tube of average radius 15 cm, whose inner walls are rough, is kept in vertical plane. A block of mass 1 kg just fit inside the tube. The speed of block is 22 m s-1, when it is introduced at the top of tube. After completing five oscillations, the block stops at the bottom region of tube. The work done by the tube on the block is ________ J. (Given 𝑔= 10 m s-2).

Q21.A projectile fired at 30° to the ground is observed to be at same height at time 3 s and 5 s after projection, during its flight. The speed of projection of the projectile is m s-1. (Given 𝑔= 10 m s-2) →

Q21.In an ac generator, a rectangular coil of 100 turns each having area 14 × 10–2 m2 is rotated at 360 rev min−1 about an axis perpendicular to a uniform magnetic field of magnitude 3. 0 T. The maximum value of the emf produced will be ______ V . [Take π = 227 ]

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.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 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.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 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.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 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 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 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 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.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 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.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.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 ________

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.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.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.

Q23.A coil has an inductance of 2 H and resistance of 4 Ω. A 10 V is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be _____ ×10−2 J

Q23.Solid sphere 𝐴 is rotating about an axis 𝑃𝑄. If the radius of the sphere is 5 cm, then its radius of gyration about 𝑃𝑄 will be √𝑥 cm. The value of 𝑥 is _____.

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.The general displacement of a simple harmonic oscillator is 𝑥= 𝐴 sin 𝜔𝑡. Let 𝑇 be its time period. The 𝑇 slope of its potential energy (𝑈) – time (𝑡) curve will be maximum when 𝑡= 𝛽. The value of 𝛽 is ______.