Electrostatics PYQs Set 6 (PDF)

Set 6 of 12 · Questions 151-180 of 349

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Mere Teacher · Previous Year Questions NEET Physics · Electrostatics · Set 6 (Q151-180)
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151. $A particle of charge ' -q ' and mass ' m' moves in a circle of radius ' r ' around an infinitely long line charge of linear density ' +λ '. Then time period will be given as: (Consider k as Coulomb's constant)$ (1) $T^{2} = \frac{4 π ^{2} m}{2 kλq} r^{3}$ (2) $T = 2 πr \frac{m}{2 kλq}$ (3) $T = \frac{1}{2 πr} \frac{m}{2 kλq}$ (4) $T = \frac{1}{2 π} \frac{2 kλq}{m}$ 152. $Some charge is being given to a conductor. Then its potential is$ (1) $maximum at surface$ (2) $maximum at center$ (3) $remain same throughout the conductor$ (4) $maximum somewhere between surface and center.$ 153. $An α-particle of mass 6.4 \times 10^{- 27} kg and charge 3.2 \times 10^{- 19} C is situated in a uniform electric field of 1.6 \times 10^{5} V m^{- 1} . The velocity of the particle at the end of 2 \times 10^{- 2} m path when it starts from rest is$ (1) $23 \times 10^{5} ms^{- 1}$ (2) $8 \times 10^{5} m s^{- 1}$ (3) $16 \times 10^{5} m s^{- 1}$ (4) $42 \times 10^{5} m s^{- 1}$ 154. $The electrostatic potential in a charged spherical region of radius r varies as V = a r^{3} + b, where a and b are constants. The total charge in the sphere of unit radius is α \times πa \in_{o} . The value of α is____. (permittivity of vacuum is ϵ_{0})$ (1) $-9$ (2) $-12$ (3) $-8$ (4) $-6$ 155. $Force between two point charges q_{1} and q_{2} placed in vacuum at 'r' cm apart is F. Force between them when placed in a medium having dielectric K = 5 at ' r /5' cm apart will be:$ (1) $F /25$ (2) $5 F$ (3) $F/5$ (4) $25 F$ 156. $A charged particle of mass ' m ' and charge ' q ' is released from rest in an uniform electric field E . Neglecting the effect of gravity, the kinetic energy of the charged particle after ' t ' second is$ (1) $\frac{Eqm}{t}$ (2) $\frac{2 E ^{2} t ^{2}}{mq}$ (3) $\frac{E ^{2} q ^{2} t ^{2}}{2 m}$ (4) $\frac{E q ^{2} m}{2 t ^{2}}$ 157. $A solid metallic sphere has a charge +3Q. Concentric with this sphere is a conducting spherical shell having charge -Q. The radius of the sphere is ' A ' and that of the spherical shell is ' B ' (B > A) . The electric field at a distance ' R ' (A < R < B) from the centre is (ϵ_{0} = permittivity of vacuum)$ (1) $\frac{Q}{2 π ϵ _{0} R}$ (2) $\frac{3 Q}{2 π ϵ _{0} R}$ (3) $\frac{3 Q}{4 π ϵ _{0} R ^{2}}$ (4) $\frac{4 Q}{2 π ϵ _{0} R ^{2}}$ 158. $An electric dipole of moment is at the origin (0, 0, 0) . The electric field due to this dipole at r \to= (+ i^+ 3 j^+ 5 k^) note that r \to \cdot p \to= 0 is parallel to$ (1) $i^+ 3 j^- 2 k^$ (2) $3 i^+ j^+ 2 k^$ (3) $- 3 i^- j^- 2 k^$ (4) $- i^+ 3 j^+ 2 k^$ 159. $The angle between the dipole moment and electric field at any point on the equatorial plane is$ (1) $90^{\circ}$ (2) $45^{\circ}$ (3) $0^{\circ}$ (4) $180^{\circ}$ 160. $The electric field intensity at a point on the axis of an electric dipole in air is 4 NC^{- 1} . Then the electric field intensity at a point on the equatorial line which is at a distance equal to twice the distance on the axial line and if the dipole is in a medium of dielectric constant 4 is$ (1) $1 NC^{- 1}$ (2) $\frac{1}{8} NC^{- 1}$ (3) $16 NC^{- 1}$ (4) $\frac{1}{16} NC^{- 1}$ 161. $Polar molecules are the molecules [NEET 2021]$ (1) $having zero dipole moment$ (2) $acquire a dipole moment only in the presence of electric field due to displacement of charges.$ (3) $acquire a dipole moment only when magnetic field is absent$ (4) $having a permanent electric dipole moment$ 162. $Consider two charged metallic spheres S1 and S2 of radii R_{1} and R_{2}, respectively. The electric fields E_{1} (on S1) and E_{2} (on S2) on their surfaces are such that E_{1} / E_{2} = R_{1} / R_{2} . Then the ratio V_{1} (on S1) / V_{2} (on S2) of the electrostatic potentials on each sphere is$ (1) $\frac{r _{1}}{r _{2}}$ (2) $(\frac{r _{1}}{r _{2}})^{2}$ (3) $\frac{r _{2}}{r _{1}}$ (4) $(\frac{r _{2}}{r _{1}})^{2}$ 163. $Electric potential at a point P due to a point charge of 5 x 10-9 C is 50 V. The distance of P from the point charge is: (Assume, \frac{1}{4 π ϵ _{0}} = 9 x 109 N m^{2} C^{- 2})$ (1) $9 cm$ (2) $3 cm$ (3) $0. 9 cm$ (4) $90 cm$ 164. $Two metal plates are separated by 2 cm . The potentials of the plates are - 10 V and + 30 V . The electric field between the two plates is$ (1) $2000 V m^{- 1}$ (2) $500 V m^{- 1}$ (3) $3000 V m^{- 1}$ (4) $1000 V m^{- 1}$ 165. $Consider two identical metallic spheres of radius R each having charge Q and mass m . Their centers have an initial separation of 4 R . Both the spheres are given an initial speed of u towards each other. The minimum value of u, so that they can just touch each other is : (Take k = \frac{1}{4 π ϵ _{0}} and assume k Q^{2} > G m^{2} where G is the Gravitational constant)$ (1) $\frac{k Q ^{2}}{2 mR} (1 - \frac{G m ^{2}}{k Q ^{2}})$ (2) $\frac{k Q ^{2}}{4 mR} (1 - \frac{G m ^{2}}{k Q ^{2}})$ (3) $\frac{k Q ^{2}}{2 mR} (1 - \frac{G m ^{2}}{2 k Q ^{2}})$ (4) $\frac{k Q ^{2}}{4 mR} (1 + \frac{G m ^{2}}{k Q ^{2}})$ 166. $Two parallel metal plates having charges +Q and -Q face each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will$ (1) $become zero$ (2) $increase$ (3) $decrease$ (4) $remain same$ 167. $An electric dipole of mass m, charge q, and length l is placed in a uniform electric field E E_{0} i . When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:$ (1) $\frac{1}{2 π} \frac{ml}{2 q E _{0}}$ (2) $2 π \frac{ml}{qE}$ (3) $\frac{1}{2 π} \frac{2 ml}{qE}$ (4) $2 π \frac{ml}{2 q E _{0}}$ 168. $The electric field and electric potential at a point due to a point charge are 500 NC^{- 1} and 30 V respectively, then the magnitude of the charge is$ (1) $1.3 \times 10^{- 9} C$ (2) $3 \times 10^{- 12} C$ (3) $2 \times 10^{- 10} C$ (4) $1.6 \times 10^{- 20} C$ 169. $The electric field in a region is given by E = (Ax + B) i, where E is in N C^{- 1} and x is in meters. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is V_{1} and that at x = - 5 is V_{2} , then V_{1} - V_{2} is:-$ (1) $320 V$ (2) $-48V$ (3) $180 V$ (4) $-520 V$ 170. $A 60, μF parallel plate capacitor whose plates are separated by 6 mm is charged to 250 V, and then the charging source is removed. When a slab of dielectric constant 5 and thickness 3 mm is placed between the plates, find the change in the potential difference across the capacitor.$ (1) $250 V$ (2) $100 V$ (3) $150 V$ (4) $75 V$ 171. $Two identical charged particles each having a mass 10 g and charge 2.0 x 1 0^{- 7} C area placed on a horizontal table with a separation of L between then such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.25, find the value of L. [Use g = 10 m s^{- 2}]$ (1) $12 cm$ (2) $10 cm$ (3) $8 cm$ (4) $5 cm$ 172. $A point charge of 10^{- 8} C is placed at origin. The work done in moving a point charge 2 μC from point A (4, 4, 2) m to B (2, 2, 1) m is____J. (\frac{1}{4 π ϵ _{o}} = 9 \times 10^{9}) in SI units)$ (1) $45 \times 10^{- 6}$ (2) $15 \times 10^{- 6}$ (3) $0$ (4) $30 \times 10^{- 6}$ 173. $A dipole of dipole moment p is placed in uniform electric field E then torque acting on it is given by$ (1) $τ = p \cdot E$ (2) $τ = p \times E$ (3) $τ = p + E$ (4) $τ = p - E$ 174. $An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively$ (1) $2q . E and minimum$ (2) $q . E and p. E$ (3) $zero and minimum$ (4) $q . E and maximum$ 175. $Two identical electric point dipoles have dipole moments p_{1} \to= p i^and p_{2} \to= - p i^and are held on the x axis at distance 'a' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely far apart is$ (1) $\frac{p}{a} \frac{1}{2 π ϵ _{0} ma}$ (2) $\frac{p}{a} \frac{2}{π ϵ _{0} ma}$ (3) $\frac{p}{a} \frac{1}{π ϵ _{0} ma}$ (4) $\frac{p}{a} \frac{3}{2 π ϵ _{0} ma}$ 176. $Consider a circular loop that is uniformly charged and has a radius a 2 . Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy plane at the origin:$ (1) $a$ (2) $a /2$ (3) $0$ (4) $a / 2$ 177. $Given below are two statements: one is labelled a Assertion (A) and the other is labelled as Reason(R) Assertion (A): Work done by electric field on moving a positive charge on an equipotential surface is always zero. Reason (R): Electric lines of forces are always perpendicular to equipotential surfaces. In the light of the above statements, choose the most appropriate answer from the options given below:$ (1) $Both (A) and (R) are correct but (R) is not the correct explanation of (A)$ (2) $((A) is correct but (R) is not correct$ (3) $(A) is not correct but (R) is correct$ (4) $Both (A) and (R) are correct and (R) is the correct explanation of (A)$ 178. $Four equal point charges Q each are placed in the xy plane at (0, 2) (4, 2) (4, - 2) and (0, - 2) . The work required to put a fifth Q at the origin of the coordinate system will be:$ (1) $\frac{Q ^{2}}{4 π \in _{0}} (1 + \frac{1}{3})$ (2) $\frac{Q ^{2}}{4 π \in _{0}} (1 + \frac{1}{5})$ (3) $\frac{Q ^{2}}{2 2 π \in _{0}}$ (4) $\frac{Q ^{2}}{4 π \in _{0}}$ 179. $A point charge 2 x 1 0^{- 2} C is moved from P to S in a uniform electric field of 30 N C^{- 1} directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be$ (1) $1200mJ$ (2) $600mJ$ (3) $-600mJ$ (4) $-l200mJ$ 180. $A cube of side L has point charges +q located at its seven vertices and -q at remsing one vertex. The electric field at its centre is found to be \| E \| = α (\frac{q}{4 π ϵ _{0} L ^{2}}) . The magnitude of constant α is$ (1) $\frac{4}{3}$ (2) $\frac{8}{3}$ (3) $3$ (4) $1$