Gauss's Law PYQs Set 2 (PDF)

Set 2 of 4 · Questions 31-60 of 113

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Mere Teacher · Previous Year Questions JEE Main Physics · Gauss's Law · Set 2 (Q31-60)
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31. $A positively charged glass rod is brought near uncharged metal sphere, which is mounted on an insulated stand. If the glass rod is removed, the net charge on the metal sphere is$ (1) $negative charge$ (2) $zero$ (3) $1.6 \times 10^{- 19} C$ (4) $positive charge$ 32. $A comb run through one's dry hair attracts small bits of paper. This is due to$ (1) $comb is a good conductor$ (2) $paper is a good conductor$ (3) $the atoms in the paper get polarised by the charged comb$ (4) $the comb possesses magnetic properties.$ 33. $A hollow metal sphere of radius 15 cm is charged such that potential on its surface is 20 V . Then, the potential at the center of sphere is$ (1) $0 V$ (2) $20 V$ (3) $10 V$ (4) $15 V$ 34. $Two metal spheres have their radii in the ratio of 4 : 7 . They are put in contact and a charge 8.8 \times 10^{- 7} C is given to the system. Then they are separated so that each can exert no influence on the other. The potential due to the smaller sphere at 60 m from it in Volt is$ (1) $85$ (2) $76$ (3) $48$ (4) $66$ 35. $An infinite line charge produces a field of 9 \times 10^{4} NC^{- 1} at a distance of 2 cm . The linear charge density is$ (1) $10^{- 7} C m^{- 1}$ (2) $1.5\times 1 0^{- 7} Cm-1$ (3) $10^{- 8} C m^{- 1}$ (4) $1.5\times 1 0^{- 8} Cm-1$ 36. $Twenty seven drops of same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop. [NEET 2021]$ (1) $660 V$ (2) $1320 V$ (3) $1520 V$ (4) $1980 V$ 37. $A charge Q is to be divided between two objects. The values of the charges on the objects so that the electrostatic force between them will be maximum is$ (1) $\frac{Q}{2}, \frac{Q}{2}$ (2) $\frac{Q}{3}, \frac{2}{3} Q$ (3) $\frac{Q}{4}, \frac{3}{4} Q$ (4) $\frac{Q}{5}, \frac{4}{5} Q$ 38. $Consider the force F on a charge 'q' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is placed at distance r from the center of the shell?$ (1) $F = \frac{1}{4 π} \frac{Qq}{- 2} for all r$ (2) $\frac{1}{4 π ϵ _{0}} \frac{qQ}{R ^{2}} > F > 0 for r<R$ (3) $F = \frac{1}{4 π ϵ _{0}} \frac{Qq}{r ^{2}} for r > R$ (4) $F = \frac{1}{4 π ϵ _{0}} \frac{Qq}{R ^{2}} for r<R$ 39. $A solid sphere of radius r_{1} = 1 cm carries charge distributed uniformly over it with density ρ_{1} = - 3 C / cm^{3} . It is surrounded by a concentric spherical shell of radius r_{2} = 2 cm carrying uniform charge density ρ_{2} = \frac{1}{2} C / cm^{2} . If ED denotes the magnitude of the electric field at distance d from the common centre of the sphere, then$ (1) $Ed = \frac{1}{3 ϵ _{0} d ^{2}}, d \leq 1 cm$ (2) $Ed = \frac{1}{ϵ _{0} d ^{2}}, d \leq 1 cm$ (3) $Ed = \frac{d}{3 ϵ _{0}} d \leq 1 cm$ (4) $Ed = \frac{d}{ϵ _{0}}, d \leq 1 cm$ 40. $Two isolated concentric, conducting spherical shells have radii R and 2R and uniform charges q and 2q respectively. If V_{1} and V_{2} are potentials at points located at distance 3R and \frac{R}{2}, respectively, from the centre of shells. Then the ratio of (\frac{V _{2}}{V _{1}}) will be$ (1) $2$ (2) $1$ (3) $\frac{1}{2}$ (4) $0$ 41. $A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μC m^{- 2} . The charge on the sphere is nearly$ (1) $2.5 \times 10^{- 3} C$ (2) $1.45 \times 10^{- 3} C$ (3) $6.5 \times 10^{- 3} C$ (4) $0.15 \times 10^{- 3} C$ 42. $There is a uniform spherically surface charge density at a distance R_{0} from the origin he charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V (R (t)) of the distribution as a function of its instantaneous radius R (t) is:$ (1) (2) (3) (4) 43. $Flux coming out from a unit positive charge kept in air is$ (1) $ϵ_{0}$ (2) $(ϵ_{0})^{- 1}$ (3) $(4 π ϵ_{0})^{- 1}$ (4) $4 π ϵ_{o}$ 44. $Two metallic spheres of radii 1 cm and 3 cm are given charges of -1\times 1 0^{-2} C and 5\times 1 0^{-2} C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is:$ (1) $2\times 1 0^{-2} C$ (2) $3\times 1 0^{-2} C$ (3) $4\times 1 0^{-2} C$ (4) $1\times 1 0^{-2} C$ 45. $Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by ρ (r) = kr, where r is the distance from the centre. Two charges A and B, of -Q each, are placed on diametrically opposite points, at equal distance, a form the centre. If A and B do not experience any force, then:$ (1) $a = 8^{- \frac{1}{4}} R$ (2) $a = \frac{3 R}{2 ^{\frac{1}{4}}}$ (3) $a = 2^{- \frac{1}{4}} R$ (4) $a = R / 3$ 46. $A hexagon of side 8 cm has a charge 4 μC at each of its vertices. The potential at the center of the hexagon is$ (1) $2.7 \times 10^{6} V$ (2) $7.2 \times 10^{11} V$ (3) $2.5 \times 10^{12} V$ (4) $3.4 \times 10^{4} V$ 47. $An electric dipole is placed on x-axis in proximity to a line charge of linear charge density 3. 0 x 1 0^{- 6} C/m. Line charge is placed on z-axis and positive and negative charge of dipole is at a distance 10mm of and 12mm from the origin respectively. If total force of 4N is exerted on the dipole, find out the amount of positive or negative charge of the dipole.$ (1) $815.1nC$ (2) $8.8µC$ (3) $0.485mC$ (4) $4.44µC$ 48. $A sphere encloses an electric dipole with charge \pm 3 \times 10^{- 6} C . What is the total electric flux across the sphere? [NEET 2019]$ (1) $- 3 \times 10^{- 6} N - m^{2} / C$ (2) $zero$ (3) $3 \times 10^{6} N - m^{2} / C$ (4) $6 \times 10^{- 6} N - m^{2} / C$ 49. $Three concentric spherical shells have radii a, b and c (a < b < c) and have surface charge densities σ, - σ and σ respectively. If V_{A}, V_{B} and V_{C} denote the potentials of the three shells, then, for c = a + b, we have$ (1) $V_{C} = V_{B} \neq = V_{A}$ (2) $V_{C} \neq = V_{B} \neq = V_{A}$ (3) $V_{C} = V_{B} = V_{A}$ (4) $V_{C} = V_{A} \neq = V_{B}$ 50. $Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become:$ (1) $(\frac{r}{3 2})$ (2) $(\frac{2 r}{3})$ (3) $(\frac{2 r}{3})$ (4) $(\frac{r}{2})^{2}$ 51. $Let V_{1} be the potential at the center of the square of side 1 m when the charges at the 4 corners are 2C each. If the same charges are placed at the corners of a square of side 2 m, then the potential at the centre of this square is V_{2} . The value of \frac{V _{2}}{V _{1}} is$ (1) $\frac{1}{2}$ (2) $\frac{1}{2}$ (3) $\frac{1}{2 2}$ (4) $\frac{1}{4 2}$ 52. $Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance d (d ≪ l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then, v varies as a function of the distance x between the sphere, as [NEET 2016]$ (1) $v \propto x$ (2) $v \propto x^{- 1/2} .$ (3) $v \propto x^{- 1}$ (4) $v \propto x^{1/2}$ 53. $The space between the two large parallel plates is filled with a material of uniform charge density ρ. Assume that one of the plate is kept at x = 0 . The potential at any point x between these plates is given by ( A and B are constants).$ (1) $- \frac{ρ x ^{3}}{2 ϵ _{0}}$ (2) $- (\frac{ρ x ^{2}}{2 ϵ _{0}} + Ax)$ (3) $- (\frac{ρ x ^{2}}{2 ϵ _{0}} + Ax + B)$ (4) $- (\frac{ρ x ^{3}}{4 ϵ _{0}} + A x^{2} + Bx)$ 54. $A thin spherical shell is charged by some source. The potential difference between the two points C and P (in V) shown in the figure is (Take, \frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} SI units) [NEET 2024]$ (1) $3 \times 10^{5}$ (2) $1 \times 10^{5}$ (3) $0.5 \times 10^{5}$ (4) $zero$ 55. $Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densities on them?$ (1) $σ_{1} = \frac{5}{6} σ, σ_{2} = \frac{5}{6} σ$ (2) $σ_{1} = \frac{5}{2} σ, σ_{2} = \frac{5}{6} σ$ (3) $σ_{1} = \frac{5}{2} σ, σ_{2} = \frac{5}{3} σ$ (4) $σ_{1} = \frac{5}{3} σ, σ_{2} = \frac{5}{6} σ$ 56. $Two small conducting balls of identical mass 20 g and identical charge 10^{- 10} C hang from non-conducting threads of length, L = 300 cm . If the equilibrium separation of balls is x and x ≪ L then the magnitude of x is (Assume, 4 π ϵ_{0} = \frac{1}{9 \times 10 ^{9}} F / m and g = 10 m / s^{2})$ (1) $\frac{2}{5 ^{1/3}} mm$ (2) $\frac{3}{10 ^{1/3}} mm$ (3) $\frac{3 ^{1/3}}{10} mm$ (4) $\frac{3 ^{2/3}}{5} mm$ 57. $A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field E though the shaded area is:$ (1) $\frac{q}{48 ϵ _{0}}$ (2) $\frac{q}{8 ϵ _{0}}$ (3) $\frac{q}{24 ϵ _{0}}$ (4) $\frac{q}{4 ϵ _{0}}$ 58. $A solid sphere of radius R carries a positive charge Q distributed uniformly throughout its volume. A very thin hole is drilled through it's center. A particle of mass m and charge - q performs simple harmonic motion about the center of the sphere in this hole. The frequency of oscillation is$ (1) $\frac{1}{2 π} (\frac{Qq}{4 π ϵ _{0} R ^{3} m})^{\frac{1}{2}}$ (2) $\frac{1}{2 π} (\frac{Qq}{4 π ϵ _{0} R ^{2} m})^{\frac{1}{2}}$ (3) $\frac{1}{2 π} \frac{Q}{( 4 π ϵ _{0} mR ^{3} ) ^{\frac{1}{2}}}$ (4) $\frac{1}{2 π} (\frac{Qq}{4 π ϵ _{0} mR})^{\frac{1}{2}}$ 59. $Two charges are + 10 μC and - 10 μC are separated by 10 cm . The magnitude of force acting on another charge 5 μC placed at the midpoint of the line joining the two charges will be [Use \frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} in SI unit]$ (1) $360 N$ (2) $0 N$ (3) $320 N$ (4) $380 N$ 60. $Charges + q and - q are placed at points A and B respectively which are a distance 2 L apart, C is the midpoint between A and B. The work done in moving a charge + Q along the semicircle CRD is$ (1) $\frac{qQ}{2 π ϵ _{0} L}$ (2) $\frac{qQ}{6 π ϵ _{0} L}$ (3) $- \frac{qQ}{6 π ϵ _{0} L}$ (4) $\frac{qQ}{4 π ϵ _{0} L}$