Title Physics ÔÇó Final Step-B ÔÇó VMC.pdf ✅

Vidyamandir Classes VMC | Final Step | Part - B 1 Class XII | Physics Final Step | Part - B | Physics Electrostatics CHOOSE THE CORRECT ALTERNATIVE. ONLY ONE CHOICE IS CORRECT. HOWEVER, QUESTIONS MARKED ‘*’ MAY HAVE MORE THAN ONE CORRECT OPTION. 1. A simple pendulum of length l has a bob of mass m, with a charge q on it A vertical sheet of charge, with surface charge density  passes through the points of suspension. At equilibrium, the string makes an angle  with the vertical, then : (A) 0 tan 2 q mg     (B) 0 tan q mg     (C) 0 cot 2 q mg     (D) 0 cot q mg     2. A charged particle of mass m and charge q is released from rest in an electric field of constant magnitude E. the kinetic energy of the particle after time t will be : (A) 2 2 2E t mq (B) 2 2 2 Eq m t (C) 2 2 2 2 E q t m (D) 2 Eqm t 3. A charge Q is distributed over two concentric hollow spheres of radius r and R (> r) such that the surface densities are equal. The potential at the common centre is: (A) 2 2 0 ( ) 4 ( ) Q R r R r    (B) Q R r  (C) Zero (D) 2 2 0 ( ) 4 ( ) Q R r R r    *4. If  0    s E .dS over a surface, then : (A) The electric field inside the surface and on it is zero (B) The electric field inside the surface is necessarily uniform (C) The number of flux lines entering the surface must be equal to the number of flux lines leaving it (D) Net charge, if any, must necessarily be outside the surface 5. The ratio of the forces between two small spheres with same charges when they are in air to when they are in a medium of dielectric constant K is : (A) 1: K (B) K :1 (C) 2 1: K (D) 2 K :1 6. Two point charges 2q and 8q are placed at a distance r apart. Where should a third charge q be placed between them so that the electrical potential energy of the system is a minimum : (A) At a distance of r/3 from 2q (B) At a distance of 2r/3 from 2q (C) At a distance of r/16 from 2q (D) None of these 7. A spherical conductor A of radius r placed concentrically inside a conducting shell B of radius R R r   . A charge Q is given to A, and then A is joined to B by a metal wire. The charge flowing from A and B will be : (A) R Q R r        (B) r Q R r        (C) Q (D) Zero
Vidyamandir Classes VMC | Final Step | Part - B 2 Class XII | Physics 8. A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at distance L from the end A is : (A) 8 0 Q  L (B) 0 3 4 Q  L (C) 4 ln 2 0 Q  L (D) 0 ln 2 4 Q  L *9. If a conductor has a potential V  0 and there are no charges anywhere else outside, then : (A) There must be charges on the surface or inside itself (B) There cannot be any charge in the body of the conductor (C) There must be charges only on the surface (D) There must be charges inside the surface 10. A non-conducting ring of radius R has charge Q distributed uniformly over it. If rotates with an angular velocity , the equivalent current will be : (A) Zero (B) Q (C) 2 Q   (D) 2 Q R   11. Four equal charge Q are placed at the four corners of a square of side a. the work done in removing a charge Q from the centre of the square to infinity is : (A) Zero (B) 2 0 2 4 Q  a (C) 2 0 2Q  a (D) 2 2 0 Q  a 12. Two charges each equal to q, are kept at x = – a and x = a on the x-axis. A particle of mass m and charge q0 = q/2 is placed at the origin. If charge q0 is given, a small displacement y(y << a) along the y-axis, the net force acting on the particle is proportional to : (A) y (B) y (C) 1/y (D) 1/ y 13. Suppose the electrostatic potential at some points in space are given by 2 V x x   ( 2 ). the electrostatic field strength at x  1 is : (A) Zero (B) 2 (C) 2 (D) 4 *14. In a region of constant potential : (A) The electric field is uniform (B) The electric field is zero (C) There can be no charge inside the region (D) The electric field shall necessarily change if a charge is placed outside the region 15. An electric dipole is placed at an angle of 30 to a non-uniform electric field. The dipole will experience (A) A translational force only in the direction of the field. (B) A translational force only in the direction normal to the direction of the field. (C) A torque as well as a translational force. (D) A torque only 16. Three charges 1 2 3    q q and q , are placed as shown in the figure. The x-component of the force on 1 q is proportional to : (A) 2 3 2 2 cos q q b a   (B) 2 3 2 2 sin q q b a   (C) 2 3 2 2 cos q q b a   (D) 2 3 2 2 sin q q b a  
Vidyamandir Classes VMC | Final Step | Part - B 3 Class XII | Physics 17. A point charge q and a charge q are placed at x a   and x a   , respectively, which of the following represents a part of E-x graph ? (A) (B) (C) (D) All of these 18. An electric dipole of common P  is placed at the origin along the x – axis. The electric field at a point P, whole position vector makes an angle  with the x – axis, will make an angle : (A)  (B)  (C)    (D) 2   with the x-axis, where 1 tan tan 2    19. A charge q is placed at a distance a/2 above the centre of a horizontal square surface of edge a as shown in figure. The electric flux through the square surface is : (A) 0 Q / 2 (B) 0 Q /  (C) 0 Q / 6 (D) 0 Q /8 20. A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at a point P at a distance R/2 from the centre of the shell is : (A) 0 2 4 Q  R (B) 0 0 2 2 4 4 Q q R R    (C) 0 0 2 4 4 Q q R R    (D) 0 ( ) 2 4 q Q R   *21. The work done to move a charge along an equipotential from A to B : (A) cannot be defined as B A  E.d   (B) must be defined as    B A E.d (C) is zero (D) can have a non-zero value 22. In figure shown, conducting shells A and B have charges Q and 2Q distributed uniformly over A and B. The value of V V A B  is : (A) 4 0 Q  R (B) 8 0 Q  R (C) 0 3 4 Q  R (D) 0 3 8 Q  R 23. The region between two concentric spheres of radii ‘a’ and ‘b’, respectively (see figure), has volume charge density A r   where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is : (A) 2 2 Q  a (B) 2 2 2 ( ) Q  b a  (C) 2 2 2 ( ) Q  a b  (D) 2 2Q  a
Vidyamandir Classes VMC | Final Step | Part - B 4 Class XII | Physics 24. A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is: (A) Zero everywhere (B) Non-zero and uniform (C) Non-uniform (D) Zero only at its centre 25. Within a spherical charge distribution of charge density ( ), r N equipotential surfaces of potential 0 0 V V V ,   , 0 0 V V V N V V    2Δ , ....... Δ (Δ 0) , are drawn and have increasing radii r0, r1, r2, ..... rN, respectively. If the difference in the radii of the surfaces is constant for all values of V0 and ΔV then : (A) ( )r  constant (B) 2 1 ( )r r   (C) 1 ( )r r   (D) ( )r r  *26. If there were only one type of charge in the universe, then : (A) 0 s E.dS   on any surface (B) 0 s E.dS   if the charge is outside the surface (C) s E.dS  could not be defined (D) 0 s q E.dS    if charges of magnitude q were inside the surface 27. A long cylindrical shell carries positive surface charge  in the upper half and negative surface charge  in the lower half. The electric field lines around the cylinder will look like figure given in : (Figures are schematics and not drawn to scale) (A) (B) (C) (D) 28. A thin disc of radius b = 2a has a concentric hole of radius a in it (see figure). It carries uniform surface charge  on it. If the electric field on its axis at height h(h << a) from its centre is given as Ch then value of C is : (A) a 0   (B) 2a 0   (C) 4a 0   (D) 8a 0   29. A charged particle q is shot towards another charged particle Q which is fixed with a speed v. It approaches Q upto a closest distance r and then returns. If q was given a speed 2v, the closest distance of approach would be : (A) r (B) 2r (C) r/2 (D) r/4 30. Shown in the figure are two point charges +Q and –Q inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If 1 is the surface charge on the inner surface and Q1 net charge on it and  2 the surface charge on the outer surface and Q2 net charge on it then (A) 1 1 2 2       0, 0 ; 0, 0 Q Q (B) 1 1 2 2       0, 0 ; 0, 0 Q Q (C) 1 1 2 2       0, 0 ; 0, 0 Q Q (D) 1 1 2 2       0, 0 ; 0, 0 Q Q