Practice Questions

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.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.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 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 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 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 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 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.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.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 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 )

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 ______.

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.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.Given below are two statements : Statement I : Electromagnetic waves are not deflected by electric and magnetic field. Statement II : The amplitude of electric field and the magnetic field in electromagnetic waves are related to . each other as E0 = √μ0ε0 B0 In the light of the above statements, choose the correct answer from the options given below: (1) Statement I is true but statement II is false (2) Both Statement I and Statement II are true (3) Statement I is false but statement II is true (4) Both Statement I and Statement II are false

Q23.Two plates A and B have thermal conductivities 84 W m-1 K-1 and 126 W m-1 K-1 respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of A and B are kept at 100∘C and 0∘C respectively, then the temperature of the surface of contact in steady state is_____ ∘C.

Q23.In a Young’s double slit experiment, two slits are illuminated with a light of wavelength 800 nm . The line joining A1P is perpendicular to A1A2 as shown in the figure. If the first minimum is detected at P , the value of slits separation a will be : JEE Main 2023 (29 Jan Shift 1) JEE Main Previous Year Paper The distance of screen from slits D = 5 cm . (1) 0. 4 mm (2) 0. 5 mm (3) 0. 2 mm (4) 0. 1 mm

Q23.There is an air bubble of radius 1. 0 mm in a liquid of surface tension 0. 075 N m–1 and density 1000 kg m–3 at a depth of 10 cm below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _______ Pa(g = 10 m s−2).

Q23.A certain pressure '𝑃' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0 . 01% whereas the liquid gets compressed to 0 . 03%. The ratio of Bulk modulus of water to that of the liquid 3 is 𝑥. The value of 𝑥 is ______.

Q23.Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40 cm . The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is______ × 10 – 3 kg m2 .

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.

Q23.An oscillating LC circuit consists of a 75 mH inductor and a 1. 2 µF capacitor. If the maximum charge to the capacitor is 2. 7 µC. The maximum current in the circuit will be _______ mA.

Q23.Two wires each of radius 0 . 2 cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is ______10 – 6 m. [Young's modulus for steel = 2 × 1011 N m – 2 and 𝑔= 10 m s – 2] JEE Main 2023 (10 Apr Shift 1) JEE Main Previous Year Paper