Practice Questions

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 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.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 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.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 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.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 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

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 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

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.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 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.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.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 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 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.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 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.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.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 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 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.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 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.