Practice Questions

Q13.A particle executes simple harmonic motion with an amplitude of 5 cm . When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is: (1) 8π (2) 3 π 3 8 (3) 4π (4) 7 π 3 3

Q13.A uniformly charged ring of radius 3a and total charge q is placed in x‐y plane centred at origin. A point charge q is moving towards the ring along the z− axis and has speed v at z = 4a . The minimum value of v such that it crosses the origin is: JEE Main 2019 (10 Apr Shift 1) JEE Main Previous Year Paper (1) √2m ( 151 4πϵ0aq2 ) 1/2 (2) √2m ( 154 4πϵ0aq2 ) 1/2 (3) √2m ( 51 4πϵ0aq2 ) 1/2 (4) √2m ( 152 4πϵ0aq2 ) 1/2

Q14.Shown in the figure is a shell made of a conductor. It has inner radius 𝑎 and outer radius 𝑏, and carries charge 𝑄 . At its centre a dipole →𝑝 is placed as shown then: (1) Surface charge density on the inner surface of the (2) Electric field outside the shell is the same as that shell is zero everywhere. of a point charge at the centre of the shell. (3) Surface charge density on the inner surface is (4) Surface charge density on the outer surface 𝑄 ( ) depends on →𝑝. uniform and equal to 2 . 4π𝑎2 JEE Main 2019 (12 Apr Shift 1) JEE Main Previous Year Paper is kept at the origin. The potential and electric field due to this dipole on the 𝑦- axis

Q14.A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound? [Given reference intensity of sound as 10−12 W/m2 ] (1) 40 cm (2) 20 cm (3) 10 cm (4) 30 cm

Q14.Charge is distributed within a sphere of radius R with a volume charge density ρ(r) = A e−2ra , where A and a r2 are constants. If Q is the total charge of this charge distribution, the radius R is: (1) a 1 (2) 1 a Q Q 2 log( 1− 2πaA ) log( 1− 2πaA ) − 2πaA − 2πaA (3) a log(1 Q ) (4) a2 log(1 Q ) q2(−25 μC) are placed on the x -axis at x = 1 m and x = 4 m

Q14.A simple pendulum of length 1 m is oscillating with an angular frequency 10rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1rad/s and an amplitude of 10−2 m . The relative change in the angular frequency of the pendulum is best given by : (1) 10−3rad/s (2) 1rad/s (3) 10−1rad/s (4) 10−5rad/s

Q14.Two electric dipoles, A, B with respective dipole moments dA→ = −4qaˆi and dB→ = −2qaˆi are placed on the x - axis with a separation R, as shown in the figure The distance from A at which both of them produce the same potential is: (1) R (2) √2R √2 −1 √2−1 (3) √2 R (4) R √2+1 √2+1 JEE Main 2019 (10 Jan Shift 1) JEE Main Previous Year Paper

Q14.There is a uniform spherically symmetric surface charge density at a distance R0 from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V (R(t)) of the distribution as a function of its instantaneous radius R(t) is: (1) (2) (3) (4)

Q15.A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be (Assume that the highest frequency a person can hear is 20,000 Hz). (1) 7 (2) 4 (3) 6 (4) 5

Q15.Four point charges −q, + q, + q and −q are placed on y-axis at y = −2d, y = −d, and y = +2d, respectively. The magnitude of the electric field E at a point on the x-axis at x = D, with D ≫d, will behave JEE Main 2019 (09 Apr Shift 2) JEE Main Previous Year Paper as: (1) E ∝ 1 (2) E ∝ D1 D4 (3) E ∝ 1 (4) E ∝ 1 D3 D2

Q16.A parallel plate capacitor is made of two square plates of side 𝑎, separated by a distance 𝑑 𝑑≪𝑎. The lower triangular portion filled with a dielectric of dielectric constant 𝐾, as shown in the figure. Capacitance of this JEE Main 2019 (09 Jan Shift 1) JEE Main Previous Year Paper capacitor is: (1) 𝐾𝜀0𝑎2 (2) 𝐾𝜀0𝑎2 2𝑑𝐾+ 1 𝑑𝐾- 1ln⁡𝐾 (3) 𝐾𝜀0𝑎2 ln⁡𝐾 (4) 1 𝐾𝜀0𝑎2 𝑑 2 𝑑

Q16.A system of three charges are placed as shown in the figure: If D >> d, the potential energy of the system is best given by: (1) + q D2 4πϵ0 1 [−q2d −q D2Q d ] (2) 4πϵ01 [+ q2d Q d ] 2q (3) + D2 4πϵ0 1 [−q2d −q2D2Q d ] (4) 4πϵ01 [−q2d Q d ]

Q18.In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line. One may conclude that 0 (2) R(T) = R0 (1) R(T) = R0eT2/T2 T2 (3) R(T) = R0e−T2/T2 0 (4) R(T) = R0e−T20/T2

Q19.An electron, moving along the x− axis with an initial energy of 100 eV, enters a region of magnetic field → B = (1.5 × 10−3 T)ˆk at S (see figure). The field extends between x = 0 and x = 2 cm. The electron is detected at the point Q on a screen placed 8 cm away from the point S. The distance d between P and Q (on the screen) is: (electron’s charge 1.6 × 10−19 C , mass of electron = 9.1 × 10−31 kg ) (1) 1.22 cm (2) 12.87 cm (3) 11.65 cm (4) 2.25 cm

Q20.A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 N m-1 (see figure). The assembly is kept in a uniform magnetic field of 0.1 T . If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of e is N . If the mass of the strip is 50 grams, its resistance 10Ω and air drag negligible, JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper N will be close to: (1) 1000 (2) 5000 (3) 10000 (4) 50000

Q20.The region between y = 0 and y = d contains a magnetic field B = B^z. A particle of mass m and charge q mv , the acceleration of the charged particle at the point of its enters the region with a velocity →v = v^i. if d = 2qB emergence at the other side is : (1) qv m B ( 12^i −√32 ^j) (2) qvmB ( √32 ^i + 12 ^j) (3) qv B −^j+^i (4) None of the above m ( √2 )

Q21. In the above circuit, C = √32 μF, R2 = 20 Ω, L = √310 H and R1 = 10 Ω. Current in L-R1 path is I1 and in C-R2 path it is I2. The voltage of AC source is given by, V = 200√2 sin (100 t) volts. The phase difference between I1 and I2 is: (1) 60o (2) 0o (3) 30o (4) 150o

Q21.An insulating thin rod of length l has a linear charge density ρ(x) = ρ0 xl on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is: (1) π n ρ0l3 (2) n ρ0l3 4 (3) π n ρ0 l3 (4) π3 n ρ0l3

Q22.A very long solenoid of radius R is carrying current I(t) = kte−αt(k > 0), as a function of time (t ≥0). Counterclockwise current is taken to be positive. A circular conducting coil of radius 2R is placed in the equitorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by: JEE Main 2019 (09 Apr Shift 2) JEE Main Previous Year Paper (1) (2) (3) (4)

Q22.Two magnetic dipoles X and Y are placed at a separation d , with their axes perpendicular to each other. The dipole moment of Y is twice that of X . A particle of charge q is passing through their mid-point P , at angle θ = 45o with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant? ( d is much larger than the dimension of the dipole) μ0 M × q𝑣 (1) 0 (2) √2 4π d 3 2 μ0 M μ0 2M (3) × q𝑣 (4) × q𝑣 4π d 3 4π d 3 2 2

Q23.An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is 𝑎 and distance of its centre from the wire is 𝑑 𝑑≫𝑎. If the loop applies a force 𝐹 on the wire then: 2 (1) 𝐹∝𝑎 (2) 𝐹= 0 𝑑 𝑎 (3) 𝐹∝𝑎2 (4) 𝐹∝ 𝑑 𝑑3

Q24.A concave mirror has radius of curvature of 40 cm . It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to: (Refractive index of water = 1.33 ) (1) 13.4 cm (2) 8.8 cm (3) 6.7 cm (4) 11.7 cm

Q24.In figure, the optical fiber is 𝑙= 2 m long and has a diameter of d = 20 μm . If a ray of light is incident on one end of the fiber at angle θ1 = 40° , the number of reflections it makes before emerging from the other end is close to: (refractive index of fiber is 1.31 , sin 40° = 0.64 and sin-1⁡0.49 = 30° .) (1) 55000 (2) 57000 (3) 45000 (4) 66000

Q24.The magnetic field of a plane electromagnetic wave is given by B = B0ˆi[cos(kz −ωt)] + B1ˆjcos(kz + ωt) , where B0 = 3 × 10–5 T and B1 = 2 × 10–6 T . The RMS value of the force experienced by a stationary charge Q = 10–4 C at z = 0 is closest to (1) 0.1 N (2) 0.9 N (3) 3 × 10–2 N (4) 0.6 N

Q24.What is the position and nature of image formed by lens combination shown in figure? ( f1, f2 are focal lengths) (1) 40 cm from point B at right; real (2) 203 cm from point B at right, real (3) 70 cm from point B at right; real (4) 70 cm from point B at left; virtual JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper