Practice Questions

Q21.A conducting circular loop is placed in a uniform magnetic field of 0. 4 T with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of 1 mm s−1 . The magnitude of induced emf in the loop at an instant when the radius of the loop is 2 cm will be _______ μV .

Q21.A proton with a kinetic energy of 2. 0 eV moves into a region of uniform magnetic field of magnitude π 2 × 10−3 T. The angle between the direction of magnetic field and velocity of proton is 60o . The pitch of the helical path taken by the proton is ____ cm. (Take, mass of proton = 1. 6 × 10−27 kg and charge on proton = 1. 6 × 10−19 C).

Q21.A car accelerates from rest of 𝑢 m s-1. The energy spent in this process is 𝐸 J. The energy required to accelerate the car from 𝑢 m s-1 to 2𝑢 m s-1 is 𝑛𝐸 J. The value of 𝑛 is _____. JEE Main 2023 (13 Apr Shift 2) JEE Main Previous Year Paper

Q21.Vectors 𝑎 ^𝑖+ 𝑏 ^𝑗+ ^𝑘 and 2 ^𝑖- 3 ^𝑗+ 4 ^𝑘 are perpendicular to each other when 3𝑎+ 2𝑏= 7, the ratio of 𝑎 to 𝑏 is 𝑥 2. The value of 𝑥 is _____.

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.If the maximum load carried by an elevator is 1400 kg ( 600 kg-Passengers + 800 kg-elevator ) , which is moving up with a uniform speed of 3 m s-1 and the frictional force acting on it is 2000 N, then the maximum power used by the motor is _____________kW . 𝑔= 10 m s-2

Q21.The length of a metallic wire is increased by 20% and its area of cross-section is reduced by 4 % . The percentage change in resistance of the metallic wire is ________ .

Q21.A block of mass 10 kg is moving along x-axis under the action of force F = 5x N . The work done by the force in moving the block from x = 2 m to 4 m will be _______ J.

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 horse rider covers half the distance with 5 m s-1 speed. The remaining part of the distance was travelled with speed 10 m s-1 for half the time and with speed 15 m s-1 for other half of the time. The mean 𝑥 speed of the rider averaged over the whole time of motion is m s-1. The value of 𝑥 is ______. 7

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 ]

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.A metallic rod of length L is rotated with an angular speed of ω normal to a uniform magnetic field B about an axis passing through one end of rod as shown in figure. The induced emf will be : . (1) 1 B2L2ω (2) 1 BL2ω 2 4 (3) 1 BL2ω (4) 1 B2Lω 2 4

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 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.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 cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60 cm. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ______ m s-1. (Given 𝑔= 10 m s-2)

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.An inductor of inductance 2 μH is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. The value of capacitance for which maximum current is drawn into the circuit is x1 F , where the value of x is ______. (Take π = 227 )

Q22.Two long parallel wires carrying currents 8 A and 15 A in opposite directions are placed at a distance of 7 cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnitude of magnetic field at P is ______ ×10−6 T. (Given: √2 = 1. 4 )

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.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 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.