Gauss's Law PYQs Set 4 (PDF)

Set 4 of 4 · Questions 91-107 of 107

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Mere Teacher · Previous Year Questions NEET Physics · Gauss's Law · Set 4 (Q91-107)
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91. $Two small spheres of masses M_{1} and M_{2} are suspended by weightless insulating threads of lengths L_{1} and L_{2} . The spheres carry charges Q_{1} and Q_{2} respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of θ_{1} and θ_{2} as shown. Which one of the following conditions is essential, if θ_{1} = θ_{2} ?$ (1) $M_{1} \neq = M_{2}, but Q_{1} = Q_{2}$ (2) $M_{1} = M_{2}$ (3) $Q_{1} = Q_{2}$ (4) $L_{1} = L_{2}$ 92. $Two parallel infinite line charges with linear charge densities + λC / m and - λC / m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges? [NEET 2019]$ (1) $\frac{2 λ}{π ϵ _{0} R} N / C$ (2) $\frac{λ}{π ϵ _{0} R} N / C$ (3) $\frac{λ}{2 π ϵ _{0} R} N / C$ (4) $Zero$ 93. $The electric flux linked with the closed surface in Nm^{2} C^{- 1} is (ϵ_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2})$ (1) $10^{10}$ (2) $8.85 \times 10^{- 13}$ (3) $10^{12}$ (4) $10^{11}$ 94. $Three charges Q, +q and +q are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero if the value of Q is :$ (1) $+q$ (2) $\frac{- 2 q}{2 + 1}$ (3) $\frac{- q}{1 + 2}$ (4) $- 2 q$ 95. $Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance d (d << l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as$ (1) $v \propto x^{- \frac{1}{2}}$ (2) $v \propto x^{- 1}$ (3) $v \propto x^{1/2}$ (4) $v \propto x$ 96. $Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become$ (1) $(\frac{2 r}{3})$ (2) $(\frac{2 r}{3})$ (3) $(\frac{1}{2})^{2}$ (4) $(\frac{r}{3 2})$ 97. $A sphere ' 1 ' with radius R has charge q. Sphere ' 2 ' with radius 3R is far from sphere ' 1 ' and is initially uncharged. If the two spheres are now connected with a thin conducting wire, then the ratio \frac{σ _{1}}{σ _{2}} of the surface charge densities is$ (1) $2.0$ (2) $2.5$ (3) $3.0$ (4) $9.0$ 98. $In free space, a particle A of charge 1 μ C is held fixed at a point P. Another particle B of the same charge and mass 4 m g is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance of 9 mm from P is : (Take \frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9} N m^{2} C^{- 2})$ (1) $1.0 m / s$ (2) $3.0 \times 10^{4} m / s$ (3) $2.0 \times 10^{3} m / s$ (4) $1.5 \times 10^{2} m / s$ 99. $Two identical charges repel each other with a force equal to 10 gwt when they are 0.6 m apart in air. (g = 10 m s^{- 2}) . The value of each charge is$ (1) $2 mC$ (2) $2 \times 10^{- 7} mC$ (3) $2 nC$ (4) $2 μC$ 100. $A charge QμC is placed at the centre of a cube, the flux coming out from each face will be$ (1) $\frac{Q}{6 ϵ _{0}} \times 1 0^{- 6}$ (2) $\frac{Q}{6 ϵ _{0}} \times 1 0^{- 3}$ (3) $\frac{Q}{24 ϵ _{0}}$ (4) $\frac{Q}{8 ϵ _{0}}$ 101. $When a soap bubble is charged$ (1) $the radius remains the same$ (2) $its radius may increase or decrease$ (3) $its radius increases$ (4) $its radius decreases.$ 102. $A uniformly charged ring of radius 3 a and total charge q is placed in xy-plane centered at origin. A point charge q is moving towards the ring along the z-axis and has speed v at z = 4 a . The minimum value of v such that it crosses the origin is:$ (1) $\frac{2}{m} (\frac{4}{15} \frac{q ^{2}}{4 π ϵ _{0} a})^{\frac{1}{2}}$ (2) $\frac{2}{m} (\frac{1}{5} \frac{q ^{2}}{4 π ϵ _{0} a})^{\frac{1}{2}}$ (3) $\frac{2}{m} (\frac{2}{15} \frac{q ^{2}}{4 π ϵ _{0} a})^{\frac{1}{2}}$ (4) $\frac{2}{m} (\frac{1}{15} \frac{q ^{2}}{4 π ϵ _{0} a})^{\frac{1}{2}}$ 103. $Two identical metal spheres charged with + 12 μ C and - 8 μ C are kept at certain distance in air. They are brought into contact and then kept at the same distance. The ratio of the magnitudes of electrostatic forces between them before and after contact is$ (1) $24 : 1$ (2) $4 : 1$ (3) $12 : 1$ (4) $8 : 1$ 104. $A hollow metallic sphere of radius 10 cm is charged such that potential of its surface is 80 V The potential at the centre of the sphere would be$ (1) $80 V$ (2) $800 V$ (3) $zero$ (4) $8 V$ 105. $If a unit positive charge is taken from one point to another over an equipotential surface, then$ (1) $work is done on the charge$ (2) $work is done by the charge$ (3) $work done is constant$ (4) $no work is done$ 106. $Three charges Q, +q and +q and placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is:$ (1) $+ q$ (2) $\frac{- 2 q}{2 + 1}$ (3) $-2q$ (4) $\frac{- q}{1 + 2}$ 107. $Nature of equipotential surface for a point charge is$ (1) $Ellipsoid with charge at foci.$ (2) $Sphere with charge at the center of the sphere.$ (3) $Sphere with charge on the surface of the sphere.$ (4) $Plane with charge on the surface.$