Practice Questions

Q15.Two sources of sound S1 and S2 produce sound waves of same frequency 660 Hz. A listener is moving from source S1 towards S2 with a constant speed u0 m/s and he hears 10 beats/s. The velocity of sound is 330 m/s. Then, u0 equals: (1) 10.0 m/s (2) 2.5 m/s (3) 5.5 m/s (4) 15.0 m/s

Q15.The figure shows a capacitor of capacitance C connected to a battery via a switch, having a total charge Q on it, in steady-state. When the switch S is turned from position A to position B , the energy dissipated in the circuit is (1) 1 Q2 (2) 3 Q2 8 C 8 C (3) 3 Q2 (4) 5 Q2 4 C 8 C JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper

Q15.A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be: (1) Q (2) Q (a2+b2+c2) 4πϵ0(a+b+c) 4πϵ0(a3+b3+c3) (3) Q ab+bc+ca (4) Q(a+b+c) 12πϵ0 abc 4πϵ0(a2+b2+c2)

Q15.In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 μF. All values in the circuit are in μF. JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper (1) 7 μF (2) 4μF 10 (3) 7 μF (4) 6 μF 11 5

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.For a uniformly charged ring of radius 𝑅, the electric field on its axis has the largest magnitude at a distance ℎ from its centre. Then value of ℎ is: (1) 𝑅 (2) 𝑅 √2 √5 (3) 𝑅√2 (4) 𝑅

Q15.A current of 5 A passes through a copper conductor (resistivity = 1.7 × 10−8 Ω m ) of radius of cross-section 5 mm . Find the mobility of the charges if their drift velocity is 1.1 × 10−3 ms−1 . (1) 1.5 m2 V−1 s−1 (2) 1.8 m2 V−1 s−1 (3) 1.0 m2 V−1 s−1 (4) 1.3 m2 V−1 s−1

Q15.An electric field of 1000 V/m is applied to an electric dipole at angle of 45∘ . The value of electric dipole moment is 10−29C ⋅m. What is the potential energy of the electric dipole? (1) −20 × 10−18 J (2) −7 × 10−27 J (3) −10 × 10−29 J (4) −9 × 10−20 J

Q16.The galvanometer deflection, when key K1 is closed but K2 is open, equals θ0 (see figure). On closing K2 also and adjusting R2 to 5Ω, the deflection in galvanometer becomes θ05 . The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery]: (1) 12 Ω (2) 22 Ω (3) 5 Ω (4) 25 Ω

Q16.The electric field in a region is given by →E = Ax + B ^i , where E is in NC-1 and 𝑥 is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at 𝑥= 1 is V1 and that at 𝑥= - 5 is V2, then V1 - V2 is (1) 320 V (2) -520 V (3) 180 V (4) -48 V

Q16.Voltage rating of a parallel plate capacitor is 500 V . Its dielectric can withstand a maximum electric field of 106V / m . The plate area is 10-4 m2 . What is the dielectric constant if the capacitance is 15 pF ? given ϵ0 = 8.86 × 10-12C2 / Nm2 (1) 3.8 (2) 8.5 (3) 4.5 (4) 6.2

Q16.In the figure shown below, the charge on the left plate of the 10F capacitor is -30C. The charge on the right plate of the 6F capacitor is: (1) −12μC (2) +12μC (3) −18μC (4) +18μC

Q16.Seven capacitors, each of capacitance 2μF, are to be connected in a configuration to obtain an effective capacitance of ( 136 )μF. Which of the combinations, shown in figures below, will achieve the desired value? (1) (2) (3) (4)

Q16.Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d . The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants K1, K2 and K3 . The first capaciitor is filled as shown in figure I, and the second one is filled as shown in figure II . If these two modified capacitors are charged by the same potential V , the ratio of the energy stored in the two, would be ( E1 refers to capacitor I and E2 to capacitor ( II ) ): E1 9K1K2K3 ( K1K2K3 ) ( K2K3 + K3K1K1 + K1K2 ) (1) (2) E1 = = E2 ( K1K2K3 ) ( K2K3 + K3K1K1 + K1K2 ) E2 K1K2K3 K1K2K3 ( K1K2K3 ) ( K2K3 (3) E1 + K3K1K1 + K1K2 ) (4) E1 = = E2 ( K1K2K3 ) ( K2K3 + K3K1K1 + K1K2 ) E2 9K1K2K3

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.In the given circuit, an ideal voltmeter connected across the 10 Ω resistance reads 2 V . The internal resistance r , of each cell is: (1) 0 Ω (2) 1.5 Ω (3) 0.5 Ω (4) 1 Ω

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 ]

Q16.A parallel plate capacitor is of area 6 cm2 and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constant K1 = 10, K2 = 12 and K3 = 14. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be: (1) 4 (2) 36 (3) 14 (4) 12

Q16.A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants K1, K2, K3, K4 arranged as shown in the figure. The effective dielectric constant K will be: (1) K = ( K1+K2K1K2 + K3+K4K3.K4 ) (2) K = 2(K1+K2+K3+K4)(K1+K2)(K3+K4) (3) K = (K1+K4)(K2+K3) (4) K = (K1+K2)(K3+K4) 2(K1+K2+K3+K4) K1+K2+K3+K4

Q16.A source of sound S is moving with a velocity of 50 m s-1 towards a stationary observer. The observer measures the frequency of the source as 1000 Hz . What will be the apparent frequency of the source when it is moving away from the observer after crossing him? (Take velocity of sound in air is 350 m s-1 ) (1) 750 Hz (2) 857 Hz (3) 1143 Hz (4) 807 Hz

Q16.Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by ρ(r) = kr, where r is the distance from the centre. Two charges A and B , of −Q each, are placed on diametrically opposite points, at equal distance, a, from the centre. If A and B do not experience any force, then: (1) a = 3R1 (2) a = R 2 4 √3 (3) a = 2 −14 R (4) a = 8 −14 R

Q16.The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure: What is the value of current at t = 4 s? (1) 1.5 μA (2) 2μA (3) Zero (4) 3μA

Q16.Charges −q and +q , located at A and B, respectively, constitute an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y ≫2a. The charge Q experiences an electrostatic force F . If Q is now moved along the equatorial line to P′ such that OP′= ( 3y ) the force on Q will be close to ( 3y ≪2a) (1) 27F . (2) F3 . (3) 3F . (4) 9F . JEE Main 2019 (10 Jan Shift 2) JEE Main Previous Year Paper

Q16.The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V . When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed the two plates of the first capacitor. The new potential difference of the combined system is: (1) (n+1)V (2) nV (K+n) K+n (3) V (4) V K+n

Q17.An ideal battery of emf 4V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and resistance 5 Ω. The value of R, to give a potential difference of 5 mV across 10 cm of potentiometer wire, is: (1) 480 Ω (2) 495 Ω (3) 395 Ω (4) 490 Ω