Practice Questions

Q11.The specific heats, Cp and Cv of a gas of diatomic molecules, A, are given (in units of J mol−1 K−1 ) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then: (1) A has one vibrational mode and B has two (2) A has a vibrational mode but B has none. (3) Both A and B have a vibrational mode each. (4) A is rigid but B has a vibrational mode.

Q11.Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. The rod is pivoted at its center 'O' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is: (1) 1 (2) 1 2π √3km 2π √km (3) 1 (4) 1 2π √6km 2π √2km

Q12.A submarine A travelling at 18km hr-1 is being chased along the line of its velocity by another submarine B travelling at 27 km hr-1 . B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency v. The value of v is closed to (Speed of sound in water 1500 m s-1 ) (1) 504 Hz (2) 499 Hz (3) 502 Hz (4) 507 Hz

Q12.A rod of mass M and length 2L is suspended at its middle by a wire. It exhibits torsional oscillations. If two masses, each of mass m, are attached at a distance L/2 from its centre on both sides, it reduces the oscillation frequency by 20%. The value of ratio m/M is close to (1) 0.17 (2) 0.77 (3) 0.57 (4) 0.37

Q12.The temperature, at which the root mean square velocity of hydrogen molecules equals their escape their escape velocity from the earth, is closest to: [ Boltzmann Constant kB = 1.38 × 10-23 J / K Avogadro number NA = 6.02 × 1026 / kg Radius of Earth: 6.4 × 106 m Gravitational acceleration on Earth = 10 ms-2] (1) 3 × 105K (2) 650 K (3) 800 K (4) 104 K JEE Main 2019 (08 Apr Shift 2) JEE Main Previous Year Paper

Q13.A wire of length 2L, is made by joining two wires A and B of same length but different radii r and 2r and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper the number of antinodes in wire A is p and that in B is q then ratio p: q is: (1) 3 : 5 (2) 4 : 9 (3) 1 : 4 (4) 1 : 2

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.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.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)

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.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

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.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