Practice Questions

Q16.For a charged spherical ball, electrostatic potential inside the ball varies with r as V = 2ar2 + b. Here, a and b are constant and r is the distance from the center. The volume charge density inside the ball is −λaε. The value of λ is ______. ε = permittivity of medium.

Q16.As shown in figure, a cuboid lies in a region with electric field E = 2x2ˆi −4yˆj + 6ˆk N C−1 . The magnitude of charge within the cuboid is nε0 C. The value of n is ______ (if dimension of cuboid is 1 × 2 × 3 m3 )

Q16.Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R Assertion A : The beam of electrons shows wave nature and exhibit interference and diffraction. Reason R : Davisson Germer Experimentally verified the wave nature of electrons. In the light of the above statements. Choose the most appropriate answer from the options given below : (1) A is correct but R is not correct (2) A is not correct but R is correct (3) Both A and R are correct but R is Not the correct (4) Both A and R are correct and R is the correct explanation of A explanation of A

Q16.A parallel plate capacitor has plate area 40 cm2 and plates separation 2 mm . The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5 . The capacitance of the system is: (1) 24ε0 F (2) 103 ε0 F (3) 10 3 ε0 F (4) 10ε0 F

Q16.The variation of stopping potential V0 as a function of the frequency ( 𝜈) of the incident light for a metal is shown in figure. The work function of the surface is JEE Main 2023 (10 Apr Shift 2) JEE Main Previous Year Paper (1) 2 . 98 eV (2) 2 . 07 eV (3) 1 . 36 eV (4) 18 . 6 eV

Q16.In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative z- axis and magnetic field is along the positive x-axis. Then the direction of propagation of electromagnetic wave is: (1) positive z-axis (2) positive y-axis (3) at 45°angle from positive y -axis (4) negative y-axis

Q16.Two parallel plate capacitors C1 and C2 each having capacitance of 10 μF are individually charged by a 100 V D.C. source. Capacitor C1 is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor C2 is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor C1 is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be _____ V . (Assuming Dielectric constant = 10 )

Q16.The kinetic energy of an electron, 𝛼- particle and a proton are given as 4𝐾, 2𝐾 and 𝐾 respectively. The de- Broglie wavelength associated with electron ( 𝜆𝑒) , 𝛼- particle ( 𝜆𝛼) and the proton (𝜆𝑝) are as follows: (1) 𝜆𝛼= 𝜆𝑝> 𝜆𝑒 (2) 𝜆𝛼< 𝜆𝑝< 𝜆𝑒 (3) 𝜆𝛼= 𝜆𝑝< 𝜆𝑒 (4) 𝜆𝛼> 𝜆𝑝> 𝜆𝑒

Q16.Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one. Reason R : Capacitance of metallic spheres depend on the radii of spheres. In the light of the above statements, choose the correct answer from the options given below. (1) A is false but R is true (2) Both A and R are true and R is the correct explanation of A (3) A is true but R is false (4) Both A and R are true but R is not the correct explanation of A

Q16.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : If an electric dipole of dipole moment 30 × 10–5 C m is enclosed by a closed surface, the net flux coming out of the surface will be zero. Reason R : Electric dipole consists of two equal and opposite charges. In the light of above, statements, choose the correct answer from the options given below. JEE Main 2023 (12 Apr Shift 1) JEE Main Previous Year Paper (1) Both A and R are true and R is the correct (2) A is false but R is true explanation of A (3) A is true but R is false (4) Both A and R are true and R is NOT the correct explanation of A

Q16.Experimentally it is found that 12. 8 eV energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is 9 × 10−10 m. x The value of the x is: _____. ( 1 eV = 1. 6 × 10−19 J, 1 = 9 × 109 Nm2C2 and electronic charge = 1. 6 × 10−19 C) 4πε0

Q16.A point charge q1 = 4q0 is placed at origin. Another point charge q2 = −q0 is placed at x = 12 cm. Charge of proton is q0 . The proton is placed on x-axis so that the electrostatic force on the proton in zero. In this situation, the position of the proton from the origin is ______ cm.

Q16.A capacitor of capacitance C is charged to a potential V . The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is: (1) CV (2) Zero ε0 (3) 2 CV (4) CV ε0 2ε0

Q16.Given below are two statements : Statement I : If the Brewster's angle for the light propagating from air to glass is 𝜃𝐵, then Brewster's angle for the light propagating from glass to air is 𝜋 - 𝜃𝐵. 2 Statement II : The Brewster's angle for the light propagating from glass to air is tan-1𝜇g, where 𝜇g is the refractive index of glass. In the light of the above statements, choose the correct answer from the options given below : (1) Both Statements I and Statement II are true. (2) Statement I is true but Statement II is false. (3) Both Statement I and Statement II are false. (4) Statement I is false but Statement II is true.

Q17.The de Broglie wavelength of a molecule in a gas at room temperature 300 K is 𝜆1. If the temperature of the gas is increased to 600 K, then the de Broglie wavelength of the same gas molecule becomes JEE Main 2023 (10 Apr Shift 1) JEE Main Previous Year Paper 1 (1) 2𝜆1 (2) √2𝜆1 (3) 1 (4) 2𝜆1 √2𝜆1

Q17.With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is (A) directly proportional to the length of the potentiometer wire (B) directly proportional to the potential gradient of the wire (C) inversely proportional to the potential gradient of the wire (D) inversely proportional to the length of the potentiometer wire Choose the correct option for the above statements: (1) B and D only (2) A and C only (3) A only (4) C only

Q17.The equivalent resistance between A and B as shown in figure is: (1) 10 kΩ (2) 5 kΩ (3) 20 kΩ (4) 30 kΩ

Q17.A wire of resistance 160 Ω is melted and drawn in a wire of one-fourth of its length. The new resistance of the wire will be (1) 16 Ω (2) 10 Ω (3) 640 Ω (4) 40 Ω

Q17.The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by 50%. The percentage change in voltage sensitivity of the galvanometer will be : (1) 100% (2) 50% (3) 75% (4) 0% JEE Main 2023 (31 Jan Shift 2) JEE Main Previous Year Paper

Q17.A uniform metallic wire carries a current 2 A, when 3. 4 V battery is connected across it. The mass of uniform metallic wire is 8. 92 × 10−3 kg, density is 8. 92 × 103 kg m−3 and resistivity is 1. 7 × 10−8 Ω −m The length of wire is : (1) l = 6. 8 m (2) l = 10 m (3) l = 5 m (4) l = 100 m

Q17.A single slit of width a is illuminated by a monochromatic light of wavelength 600 nm . The value of a for which first minimum appears at θ = 30o on the screen will be : (1) 1. 2 μm (2) 3 μm (3) 1. 8 μm (4) 0. 6 μm

Q17.An electric dipole of dipole moment is 6. 0 × 10−6 C m placed in a uniform electric field of 1. 5 × 103 N C−1 in such a way that dipole moment is along electric field. The work done in rotating dipole by 180° in this field will be_______ mJ.

Q17.Different combination of 3 resistors of equal resistance R are shown in the figures. The increasing order for power dissipation is: (A) (B) JEE Main 2023 (13 Apr Shift 1) JEE Main Previous Year Paper (C) (D) (1) PB < PC < PD < PA (2) PC < PD < PA < PB (3) PC < PB < PA < PD (4) PA < PB < PC < PD

Q17.The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is JEE Main 2023 (06 Apr Shift 1) JEE Main Previous Year Paper (1) 𝐷 (2) 𝐴 (3) 𝐵 (4) 𝐶

Q17.As shown in the figure, two parallel plate capacitors having equal plate area of 200 cm2 are joined in such a way that a ≠b. The equivalent capacitance of the combination is xε0F . The value of x is _____.