Practice Questions

Q8. A drop of liquid of density ρ is floating half immersed in a liquid of density σ and surface tension 7. 5 × 10−4 N cm−1 . The radius of drop in cm will be : (Take : g = 10 ms−2 ) (1) 15 (2) 15 √2ρ−σ √ρ−σ (3) 3 (4) 3 2√ρ−σ 20√2ρ−σ

Q10.Two identical metallic spheres 𝐴 and 𝐵 when placed at certain distance in air repel each other with a force of 𝐹 . Another identical uncharged sphere 𝐶 is first placed in contact with 𝐴 and then in contact with 𝐵 and finally placed at midpoint between spheres 𝐴and 𝐵. The force experienced by sphere 𝐶 will be : 3𝐹 3𝐹 (1) (2) 2 4 (3) 𝐹 (4) 2𝐹

Q10.Two identical positive charges Q each are fixed at a distance of 2a apart from each other. Another point charge q0 with mass m is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge q0 executes SHM. The time period of oscillation of charge q0 will be (1) √4π3ε0ma3q0Q (2) √ 4π3ε0ma3q0Q (3) √2π2ε0ma3q0Q (4) √8π3ε0ma3q0Q

Q10.Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is √2 times the speed of sound, then the value of n will be (1) 1 (2) 2 (3) 3 (4) 4

Q11.A source of potential difference 𝑉 is connected to the combination of two identical capacitors as shown in the figure. When key 𝐾 is closed, the total energy stored across the combination is 𝐸1. Now key 𝐾 is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored 𝐸1 across the combination is now 𝐸2. The ratio will be 𝐸2 1 2 (1) (2) 10 5 5 5 (3) (4) 13 26

Q11.Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-point on the perpendicular bisector. The value of x at which charge q will experience the maximum Coulomb's force is: (1) d (2) d 2 (3) d (4) d √2 2√2

Q11.A spherically symmetric charge distribution is considered with charge density varying as ρ0( 34 −rR ) for r ≤R ρ(r) = { Zero for r > R Where, r(r < R) is the distance from the centre O (as shown in figure). The electric field at point P will be : (1) 4ε0 ρ0r ( 43 −rR ) (2) ρ0r3ε0 ( 43 −rR ) (3) ρ0r 4ε0 (1 −rR ) (4) ρ0r5ε0 (1 −rR )

Q12.A long cylindrical volume contains a uniformly distributed charge of density ρ. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is : (1) ρqR2 (2) ρqR2 4εo 2εo (3) qρ (4) 4ε0R2 4ε0R2 qρ

Q13.A small square loop of wire of side 𝑙 is placed inside a large square loop of wire 𝐿𝐿≫𝑙. Both loops are coplanar and their centres coincide at point 𝑂 as shown in figure. The mutual inductance of the system is (1) 2√2𝜇0𝐿2 (2) 𝜇0𝑙2 𝜋𝑙 2√2𝜋𝐿 (3) 𝜇0𝐿2 (4) 2√2𝜇0𝑙2 2√2𝜋𝑙 𝜋𝐿

Q13.As shown in the figure, a metallic rod of linear density 0 . 45 kg m-1 is lying horizontally on a smooth incline plane which makes an angle of 45° with the horizontal. The minimum current flowing in the rod required to keep it stationary, when 0 . 15 T magnetic field is acting on it in the vertical upward direction, will be (Use 𝑔= 10 m s-2) (1) 30 A (2) 15 A (3) 10 A (4) 3 A JEE Main 2022 (28 Jul Shift 1) JEE Main Previous Year Paper

Q14.A metal surface is illuminated by a radiation of wavelength 4500 A . The ejected photo-electron enters a constant magnetic field of 2 mT making an angle of 90° with the magnetic field. If it starts revolving in a circular path of radius 2 mm, the work function of the metal is approximately (1) 1. 36 eV (2) 1. 69 eV (3) 2. 78 eV (4) 2. 23 eV

Q14.A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be (Assume the coil to be short circuited.) (1) Doubled (2) The same (3) Quadrupled (4) Halved

Q14.A series LCR circuit has L = 0. 01 H, R = 10 Ω and C = 1 μF and it is connected to ac voltage of amplitude (Vm) 50 V . At frequency 60% lower than resonant frequency, the amplitude of current will be approximately (1) 466 mA (2) 312 mA (3) 238 mA (4) 196 mA

Q14.A velocity selector consists of electric field 𝐸= 𝐸 ^k and magnetic field 𝐵= 𝐵 ^j with 𝐵= 12 mT. The value 𝐸 required for an electron of energy 728eV moving along the positive x-axis to pass undeflected is (Given, mass of electron = 9 . 1 × 10-31 kg) (1) 192 kV m-1 (2) 192 mV m-1 (3) 9600 kV m-1 (4) 16 kV m-1

Q14.A coil of inductance 1 H and resistance 100 Ω is connected to a battery of 6 V . Determine approximately : (a) The time elapsed before the current acquires half of its steady-state value (b) The energy stored in the magnetic field associated with the coil at an instant 15 ms after the circuit is switched on. (Given ln 2 = 0. 693, e −32 = 0. 25) (1) t = 10 ms; U = 2 mJ (2) t = 10 ms; U = 1 mJ (3) t = 7 ms; U = 1 mJ (4) t = 7 ms; U = 2 mJ

Q15.Two long parallel conductors S1 and S2 are separated by a distance 10 cm and carrying currents of 4 A and 2 A respectively. The conductors are placed along x-axis in X −Y plane. There is a point P located between the conductors (as shown in figure). + m s−1 ; where ˆi & A charge particle of 3π coulomb is passing through the point P with velocity →v= (2ˆi 3ˆj) ˆj represents unit vector along x & yaxis respectively. The force acting on the charge particle is 4π × + N. The value of x is 10−5(−xˆi 2ˆj) (1) 2 (2) 1 (3) 3 (4) −3

Q15.If Electric field intensity of a uniform plane electro magnetic wave is given as E = −301. 6 sin(kz −ωt)ˆax + 452. 4 sin(kz −ωt)ˆay V m−1. Then, magnetic intensity H of this wave in A m−1 will be [Given : Speed of light in vacuum c = 3 × 108 m s−1 , Permeability of vacuum μ0 = 4π × 10−7 N A−2 ] (1) +0. 8 sin(kz −ωt)ˆay + 0. 8 sin(kz −ωt)ˆax (2) +1. 0 × 10−6 sin(kz −ωt)ˆay + 1. 5 × 10−6(kz −ωt)ˆax (3) −0. 8 sin(kz −ωt)ˆay −1. 2 sin(kz −ωt)ˆax (4) −1. 0 × 10−6 sin(kz −ωt)ˆay −1. 5 × 10−6 sin(kz −ωt)ˆa λ, then this phenomenon is called as

Q17.For an object placed at a distance 2. 4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm from the lens. A glass plate of refractive index 1. 5 and thickness 1 cm is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen? (1) 0. 8 m (2) 3. 2 m (3) 1. 2 m (4) 5. 6 m

Q21.A pendulum of length 2 m consists of a wooden bob of mass 50 g . A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed v and the bob just completes the 3 vertical circle. The value of v is _____ m s−1 (if g = 10 m s−2 ). JEE Main 2022 (27 Jun Shift 1) JEE Main Previous Year Paper

Q21.In an experiment of determine the Young's modulus of wire of a length exactly 1 m, the extension in the length of the wire is measured as 0. 4 mm with an uncertainty of ±0. 02 mm when a load of 1 kg is applied. The JEE Main 2022 (26 Jul Shift 1) JEE Main Previous Year Paper diameter of the wire is measured as 0. 4 mm with an uncertainty of ±0. 01 mm. The error in the measurement of Young's modulus (ΔY) is found to be x × 1010 N m−2 . The value of x is _____ .

Q22.A small spherical ball of radius 0. 1 mm and density 104 kg m−3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it JEE Main 2022 (29 Jun Shift 2) JEE Main Previous Year Paper continue to fall with same constant velocity inside water, then the value of h will be ____ m. (Given g = 10 m s−2 , viscosity of water = 1. 0 × 10−5 N‐s m−2 ).

Q22.A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane PQ will be 1 √xgh m s−1 . The value of x (rounded off to the nearest integer) is _____. 2

Q25.An observer is riding on a bicycle and moving towards a hill at 18 km h-1. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is 640 Hz and velocity of the sound in air is 320 m s-1, the beat frequency between the two sounds heard by observer will be _____ Hz.

Q26.The potential energy of a particle of mass 4 kg in motion along the x-axis is given by U = 4(1 −cos 4x) J. The time period of the particle for small oscillation (sin θ ≃θ) ( Kπ ) s. The value of K is _____ .

Q27.In the given circuit 'a' is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum, will be √x2 . The value of x is _____ .