Practice Questions

Q10.Consider a sphere of radius R which carries a uniform charge density ρ . If a sphere of radius R is carved out 2 −→ −−EA → → of it, as shown, the ratio of magnitude of electric field EA and EB , respectively, at points A and B due to− → EB the remaining portion is: (1) 21 (2) 18 34 34 (3) 17 (4) 18 54 54 + × 10−29 C m at the origin (0,0, 0) . The electric field due

Q11.Two identical electric point dipoles have dipole have dipole moments →p1 = pˆi and →p2 = −pˆi and are held on the x-axis at distance ' a ' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is ' m', their speed when they are infinitely far apart is : (1) P 1 (2) P 1 a √ πε0 ma a √ 2πε0 ma (3) P 2 (4) P 3 a √ πε0 ma a √ 2πε0 ma

Q12.A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q . If it acquires a speed ν when it has fallen through a vertical height y (see figure), then (assume the remaining portion to be spherical) (1) v2 = y[ 4πϵ0R2ymqQ + g] (2) v2 = y[ 4πϵ0R(R+y)mqQ + g] (3) v2 = 2y[ 4πϵ0(R+y)3mQqR + g] (4) v2 = 2y[ 4πε0R(R+y)mqQ + g] JEE Main 2020 (05 Sep Shift 1) JEE Main Previous Year Paper

Q12.A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and released, it starts JEE Main 2020 (09 Jan Shift 2) JEE Main Previous Year Paper performing simple harmonic motion of time period T. The mass of the loop is m then: (1) 2iB T = √2miB (2) T = √πm (3) iB T = √2πmiB (4) T = √πm

Q12.The figure shows a region of length ' 𝓁 ' with a uniform magnetic field of 0. 3 T in it and a proton entering the region with velocity 4 × 105 m s−1 making an angle 60° with the field. If the proton completes 10 revolution by the time it cross the region shown, ' 𝓁 ' is close to (mass of proton = 1. 67 × 10−27 kg, charge of the proton = 1. 6 × 10−19 C) (1) 0. 11 m (2) 0. 88 m (3) 0. 44 m (4) 0. 22 m

Q12.A particle of charge q and mass m is moving with a velocity −vˆi(v ≠0) → Y −Z plane at distance d. If there is magnetic field B = B0ˆk, the minimum value of v for which the particle will not hit the screen is : (1) qdB0 (2) 2qdB0 3m m (3) qdB0 (4) qdB0 m 2m

Q12.A capacitor is made of two square plates each of side ‘ a ’ making a very small angle α between them, as shown in figure. The capacitance will be close to: (1) ∈0a2 d (1 −αa2d ) (2) ∈0a2d (1 −αa4d ) (3) ∈0a2 d (1 + αad ) (4) ∈0a2d (1 −3αa2d )

Q13.Radiation, with wavelength 6561 Å falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of 3 × 10−4 T . If the radius of the largest circular path followed by the electrons is 10 mm , the work function of the metal is close to: (1) 1.6 eV (2) 0.8eV (3) 1.1 eV (4) 1.8eV

Q13.A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths a and b, then the magnitude and direction of magnetic moment of the loop ABCDEFA is : abI along + + ˆk ) (2) ˆk ) (1) √2abI along ( √2ˆj √2 ( √2ˆj √2 + + 2ˆk ) (4) ˆk ) (3) √2abI along ( √5ˆj √5 abI along ( √5ˆj √5

Q13.Consider a circular coil of wire carrying constant current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by ϕi The magnetic flux through the area of the circular coil area is given by ϕ0 . Which of the following option is correct? (1) ϕi = ϕ0 (2) ϕi > ϕ0 (3) ϕi < ϕ0 (4) ϕi = −ϕ0

Q14.A 750 Hz, 20 V(rms) source is connected to a resistance of 100 Ω, an inductance of 0. 1803 H and a capacitance of 10 μF all in series. The time in which the resistance (heat capacity 2 J/°C ) will get heated by 10°C. (assume no loss of heat to the surroundings) is close to : (1) 418 s (2) 245 s (3) 365 s (4) 348 s →

Q15.A charged particle of mass ‘ m ’ and charge ‘ q ’ moving under the influence of uniform electric field →E ˆi and a −→ uniform magnetic field B ˆk follows a trajectory from point P to Q as shown in figure. The velocities at P and Q → → are respectively, vi and −2vj . Then which of the following statements (A, B, C, D) are the correct? (Trajectory shown is schematic and not to scale) 3 mv2 (A) E = 2 ( qa ) (B) Rate of work done by the electric field at P is 32 ( mv3a ) (C) Rate of work done by both the fields at Q is zero (D) The difference between the magnitude of angular momentum of the particle at P and Q is 2mav . (1) (A), (C), (D) (2) (B), (C), (D) (3) (A), (B), (C) (4) (A), (B), (C), (D) −

Q15.A circular coil has moment of inertia 0. 8 kg m2 around any diameter and is carrying current to produce a magnetic moment of 20 Am2 . The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of 4 T is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by 60o will be : (1) 10 rad s−1 (2) 10π rad s−1 (3) 20π rad s−1 (4) 20 rad s−1

Q16.A square loop of side 2a and carrying current I is kept in xz plane with its centre at origin. A long wire carrying the same current I is placed parallel to z-axis and passing through point (0, b, 0), (b >> a). The magnitude of torque on the loop about z-axis will be : (1) 2μ0I2a2 (2) 2μ0I2a2b πb π(a2+b2) (3) μ0I2a2b (4) μ0I2a2 2π(a2+b2) 2πb

Q18.You are given that 73Li = 7. 0160u,Mass of Mass of 42He = 4. 0026u and Mass of 11He = 1. 0079H When 20g of 73Li is converted into 42 He by proton capture, the energy liberated, (in kWh ), is : [Mass of nucleon = 1 GeV /c2 ] (1) 4. 5 × 105 (2) 8 × 106 (3) 6. 82 × 105 (4) 1. 33 × 106

Q19.Given the masses of various atomic particles mP = 1, 0072 u , mn = 1, 0087 u , me = 0 .000548 u , mv = 0 , ¯¯md = 2 .0141 u , where p =proton, n ≡neutron, e ≡electron, v ≡antineutrino and d ≡deuteron. Which of the following process is allowed by momentum and energy conservation : ¯(1) n + n → deuterium atom (electron bound to the (2) p →n + e+ + v nucleus) (3) n + p →d + γ (4) e+ + e−→γ

Q21. ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid-points of AB, AC and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane ABC is I0 . If part ADE is removed, the moment of inertia of the remaining part about the same axis is NI0 where N is an integer. Value of N is: 16

Q21.A particle of mass 200 MeV c−2 collides with a hydrogen atom at rest. Soon after the collision, the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV ) is N4 . The value of N is: (Given the mass of the hydrogen atom to be 1 GeV c−2 )......... → + 2ˆj + m . Then the magnitude of torque about the point N acts at a point (4ˆi + 3ˆj −ˆk)

Q21.The sum of two forces P and Q is R such that R = P . Find the angle between resultant of 2P and Q and Q , ________ JEE Main 2020 (07 Jan Shift 2) JEE Main Previous Year Paper

Q21.A block starts moving up an inclined plane of inclination 30° with an initial velocity of v0 . It comes back to its initial position with velocity v0 2 . The value of the coefficient of kinetic friction between the block and the inclined plane is close to 1 , The nearest integer to I is : 1000

Q22. Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is μ = 0.4 , the maximum possible value of 100 × ba for a box not to topple before moving is ________

Q22.A particle of mass m is moving along the x-axis with initial velocity uˆi. It collides elastically with a particle of mass 10m at rest and then moves with half its initial kinetic energy (see figure). If sin θ1 = √n sin θ2 then value of n is ________. JEE Main 2020 (02 Sep Shift 2) JEE Main Previous Year Paper

Q23.In a series LR circuit, power of 400 W is dissipated from a source of 250 V, 50 Hz. The power factor of the circuit is 0. 8 . In order to bring the power factor to unity, a capacitor of value C is added in series to the L and R. Taking the value of C as ( 3πn ) μF , then value of n is

Q23.A wire of density 9 × 10–3 kg cm–3 is stretched between two clamps 1 m apart. The resulting strain in the wire is 4. 9 × 10–4 . The lowest frequency of the transverse vibrations in the wire (Young's modulus of wire Y = 9 × 1010 Nm–2 ), (to the nearest integer),_______

Q23.Two concentric circular coils, C1 and C2 , are placed in the XY plane. C1 has 500turns, and a radius of 1 cm . C2 has 200 turns and radius of 20 cm . C2 carries a time dependent current I(t) = (5t2 −2t + 3)A where t is in s. The emf induced in C1(in mV) at the instant t = 1 s is x4 . The value of x is ..........