Page 1 For JEE Advanced Objective Questions Single Correct Option Q 1. In the diagram shown, the charge +Q is fixed. Another charge + 2q and mass M is projected from a distance R from the fixed charge. Minimum separation between the two charges if the velocity becomes 1 3 times of the projected velocity, at this moment is (Assume gravity to be absent) (a) 3 R 2 (b) 1 R 3 (c) 1 R 2 (d) None of these Q 2. A uniform electric field of strength E ? exists in a region. An electron enters a point A with velocity v as shown. It moves through the electric field and reaches at point B. Velocity of particle at B is 2v at 30° with xaxis. Then (a) electric field 2 3mv ˆ Ei 2ea ?? ? (b) rate of doing work done by electric field at B is 3 3mv 2ea (c) Both (a) and (b) are correct (d) Both (a) and (b) are wrong Q 3. Two point charges a and b whose magnitudes are same positioned at a certain distance along the positive xaxis from each other, a is at origin. Graph is drawn between electrical field strength and distance x from a. E is taken positive if it is along the line joining from a to b. From the graph it can be decided that (a) a is positive, b is negative (b) a and b both are positive (c) a and b both are negative (d) a is negative, b is positive Note Graph is drawn only between a and b. Q 4. Six charges are placed at the vertices of a rectangular hexagon as shown in the figure. The electric field on the line passing through point O and perpendicular to the plane of the figure as a function of distance x from point O is (x >>a) Page 2 For JEE Advanced Objective Questions Single Correct Option Q 1. In the diagram shown, the charge +Q is fixed. Another charge + 2q and mass M is projected from a distance R from the fixed charge. Minimum separation between the two charges if the velocity becomes 1 3 times of the projected velocity, at this moment is (Assume gravity to be absent) (a) 3 R 2 (b) 1 R 3 (c) 1 R 2 (d) None of these Q 2. A uniform electric field of strength E ? exists in a region. An electron enters a point A with velocity v as shown. It moves through the electric field and reaches at point B. Velocity of particle at B is 2v at 30° with xaxis. Then (a) electric field 2 3mv ˆ Ei 2ea ?? ? (b) rate of doing work done by electric field at B is 3 3mv 2ea (c) Both (a) and (b) are correct (d) Both (a) and (b) are wrong Q 3. Two point charges a and b whose magnitudes are same positioned at a certain distance along the positive xaxis from each other, a is at origin. Graph is drawn between electrical field strength and distance x from a. E is taken positive if it is along the line joining from a to b. From the graph it can be decided that (a) a is positive, b is negative (b) a and b both are positive (c) a and b both are negative (d) a is negative, b is positive Note Graph is drawn only between a and b. Q 4. Six charges are placed at the vertices of a rectangular hexagon as shown in the figure. The electric field on the line passing through point O and perpendicular to the plane of the figure as a function of distance x from point O is (x >>a) (a) 0 (b) 3 0 Qa x ?? (c) 3 0 2Qa x ?? (d) 3 0 3Qa x ?? Q 5. If the electric potential of the inner shell is 10 V and that of the outer shell is 5 V, then the potential at the centre will be (a) 10 V (b) 5 V (c) 15 V (d) zero Q 6. A solid conducting sphere of radius a having a charge q is surrounded by a concentric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure. Find the amount of heat produced when switch is closed 0 1 k 4 ? ?? (a) 2 kq 2a (b) 2 kq 3a (c) 2 kq 4a (d) 2 kq 6a Q 7. There are four concentric shells A,B,C and D of radii a, 2a, 3a and 4a respectively. Shells B and D are given charges + q and  q respectively. Shell C is now earthed. The potential difference V A  V C is 0 1 k 4 ? ?? (a) kq 2a (b) kq 3a (c) kq 4a (d) kq 6a Q 8. Potential difference between centre and surface of the sphere of radius R and uniform volume charge density within it will be (a) 2 0 R 6 ? ? (b) 2 0 R 4 ? ? (c) 2 0 R 3 ? ? (d) 2 0 R 2 ? ? Page 3 For JEE Advanced Objective Questions Single Correct Option Q 1. In the diagram shown, the charge +Q is fixed. Another charge + 2q and mass M is projected from a distance R from the fixed charge. Minimum separation between the two charges if the velocity becomes 1 3 times of the projected velocity, at this moment is (Assume gravity to be absent) (a) 3 R 2 (b) 1 R 3 (c) 1 R 2 (d) None of these Q 2. A uniform electric field of strength E ? exists in a region. An electron enters a point A with velocity v as shown. It moves through the electric field and reaches at point B. Velocity of particle at B is 2v at 30° with xaxis. Then (a) electric field 2 3mv ˆ Ei 2ea ?? ? (b) rate of doing work done by electric field at B is 3 3mv 2ea (c) Both (a) and (b) are correct (d) Both (a) and (b) are wrong Q 3. Two point charges a and b whose magnitudes are same positioned at a certain distance along the positive xaxis from each other, a is at origin. Graph is drawn between electrical field strength and distance x from a. E is taken positive if it is along the line joining from a to b. From the graph it can be decided that (a) a is positive, b is negative (b) a and b both are positive (c) a and b both are negative (d) a is negative, b is positive Note Graph is drawn only between a and b. Q 4. Six charges are placed at the vertices of a rectangular hexagon as shown in the figure. The electric field on the line passing through point O and perpendicular to the plane of the figure as a function of distance x from point O is (x >>a) (a) 0 (b) 3 0 Qa x ?? (c) 3 0 2Qa x ?? (d) 3 0 3Qa x ?? Q 5. If the electric potential of the inner shell is 10 V and that of the outer shell is 5 V, then the potential at the centre will be (a) 10 V (b) 5 V (c) 15 V (d) zero Q 6. A solid conducting sphere of radius a having a charge q is surrounded by a concentric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure. Find the amount of heat produced when switch is closed 0 1 k 4 ? ?? (a) 2 kq 2a (b) 2 kq 3a (c) 2 kq 4a (d) 2 kq 6a Q 7. There are four concentric shells A,B,C and D of radii a, 2a, 3a and 4a respectively. Shells B and D are given charges + q and  q respectively. Shell C is now earthed. The potential difference V A  V C is 0 1 k 4 ? ?? (a) kq 2a (b) kq 3a (c) kq 4a (d) kq 6a Q 8. Potential difference between centre and surface of the sphere of radius R and uniform volume charge density within it will be (a) 2 0 R 6 ? ? (b) 2 0 R 4 ? ? (c) 2 0 R 3 ? ? (d) 2 0 R 2 ? ? Q 9. A positively charged disc is placed on a horizontal plane. A charged particle is released from a certain height on its axis. The particle just reaches the centre of the disc. Select the correct alternative. (a) Particle has negative charge on it (b) Total potential energy (gravitational + electrostatic) of the particle first increases then decreases (c) Total potential energy of the particle first decreases then increases (d) Total potential energy of the particle continuously decreases Q 10. The curve represents the distribution of potential along the straight line joining the two charges Q 1 and Q 2 (separated by a distance r) then which of the following statements are correct ? 1. Q 1  > Q 2  2. Q 1 is positive in nature 3. A and B are equilibrium points 4. C is a point of unstable equilibrium (a) 1 and 2 (b) 1,2 and 3 (c) 1,2 and 4 (d) 1,2, 3 and 4 Q 11. A point charge q 1 = q is placed at point P. Another point charge q 2 =q is placed at point Q. At some point R(R ? P, R ? Q), electric potential due to q 1 is V 1 and electric potential due to q 2 is V 2 . Which of the following is correct? (a) Only for some points V 1 > V 2 (b) Only for some points V 2 > V 1 (c) For all points V 1 > V 2 (d) For all points V 2 >V 1 Q 12. The variation of electric field between the two charges q 1 and q 2 along the line joining the charges is plotted against distance from q 1 (taking rightward direction of electric field as positive) as shown in the figure. Then the correct statement is (a) q 1 and q 2 are positive and q 1 < q 2 (b) q 1 and q 2 are positive and q 1 > q 2 (c) q 1 is positive and q 2 is negative q 1 <  q 2  (d) q 1 and q 2 are negative and q 1  <  q 2  Q 13. A charge q is placed at O in the cavity in a spherical uncharged conductor. Point S is outside the conductor. If q is displaced from O towards S (still remaining within the cavity) (a) electric field at S will increase (b) electric field at S will decrease (c) electric field at S will first increase and then decrease (d) electric field at S will not change Page 4 For JEE Advanced Objective Questions Single Correct Option Q 1. In the diagram shown, the charge +Q is fixed. Another charge + 2q and mass M is projected from a distance R from the fixed charge. Minimum separation between the two charges if the velocity becomes 1 3 times of the projected velocity, at this moment is (Assume gravity to be absent) (a) 3 R 2 (b) 1 R 3 (c) 1 R 2 (d) None of these Q 2. A uniform electric field of strength E ? exists in a region. An electron enters a point A with velocity v as shown. It moves through the electric field and reaches at point B. Velocity of particle at B is 2v at 30° with xaxis. Then (a) electric field 2 3mv ˆ Ei 2ea ?? ? (b) rate of doing work done by electric field at B is 3 3mv 2ea (c) Both (a) and (b) are correct (d) Both (a) and (b) are wrong Q 3. Two point charges a and b whose magnitudes are same positioned at a certain distance along the positive xaxis from each other, a is at origin. Graph is drawn between electrical field strength and distance x from a. E is taken positive if it is along the line joining from a to b. From the graph it can be decided that (a) a is positive, b is negative (b) a and b both are positive (c) a and b both are negative (d) a is negative, b is positive Note Graph is drawn only between a and b. Q 4. Six charges are placed at the vertices of a rectangular hexagon as shown in the figure. The electric field on the line passing through point O and perpendicular to the plane of the figure as a function of distance x from point O is (x >>a) (a) 0 (b) 3 0 Qa x ?? (c) 3 0 2Qa x ?? (d) 3 0 3Qa x ?? Q 5. If the electric potential of the inner shell is 10 V and that of the outer shell is 5 V, then the potential at the centre will be (a) 10 V (b) 5 V (c) 15 V (d) zero Q 6. A solid conducting sphere of radius a having a charge q is surrounded by a concentric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure. Find the amount of heat produced when switch is closed 0 1 k 4 ? ?? (a) 2 kq 2a (b) 2 kq 3a (c) 2 kq 4a (d) 2 kq 6a Q 7. There are four concentric shells A,B,C and D of radii a, 2a, 3a and 4a respectively. Shells B and D are given charges + q and  q respectively. Shell C is now earthed. The potential difference V A  V C is 0 1 k 4 ? ?? (a) kq 2a (b) kq 3a (c) kq 4a (d) kq 6a Q 8. Potential difference between centre and surface of the sphere of radius R and uniform volume charge density within it will be (a) 2 0 R 6 ? ? (b) 2 0 R 4 ? ? (c) 2 0 R 3 ? ? (d) 2 0 R 2 ? ? Q 9. A positively charged disc is placed on a horizontal plane. A charged particle is released from a certain height on its axis. The particle just reaches the centre of the disc. Select the correct alternative. (a) Particle has negative charge on it (b) Total potential energy (gravitational + electrostatic) of the particle first increases then decreases (c) Total potential energy of the particle first decreases then increases (d) Total potential energy of the particle continuously decreases Q 10. The curve represents the distribution of potential along the straight line joining the two charges Q 1 and Q 2 (separated by a distance r) then which of the following statements are correct ? 1. Q 1  > Q 2  2. Q 1 is positive in nature 3. A and B are equilibrium points 4. C is a point of unstable equilibrium (a) 1 and 2 (b) 1,2 and 3 (c) 1,2 and 4 (d) 1,2, 3 and 4 Q 11. A point charge q 1 = q is placed at point P. Another point charge q 2 =q is placed at point Q. At some point R(R ? P, R ? Q), electric potential due to q 1 is V 1 and electric potential due to q 2 is V 2 . Which of the following is correct? (a) Only for some points V 1 > V 2 (b) Only for some points V 2 > V 1 (c) For all points V 1 > V 2 (d) For all points V 2 >V 1 Q 12. The variation of electric field between the two charges q 1 and q 2 along the line joining the charges is plotted against distance from q 1 (taking rightward direction of electric field as positive) as shown in the figure. Then the correct statement is (a) q 1 and q 2 are positive and q 1 < q 2 (b) q 1 and q 2 are positive and q 1 > q 2 (c) q 1 is positive and q 2 is negative q 1 <  q 2  (d) q 1 and q 2 are negative and q 1  <  q 2  Q 13. A charge q is placed at O in the cavity in a spherical uncharged conductor. Point S is outside the conductor. If q is displaced from O towards S (still remaining within the cavity) (a) electric field at S will increase (b) electric field at S will decrease (c) electric field at S will first increase and then decrease (d) electric field at S will not change Q 14. A uniform electric field of 400 V/m is directed at 45° above the xaxis as shown in the figure. The potential difference V A  V B is given by (a) 0 (b) 4 V (c) 6.4 V (d) 2.8 V Q 15. Initially the spheres A and B are at potential V A and V B respectively. Now sphere B is earthed by closing the switch. The potential of A will now become (a) 0 (b) V A (c)V A  V B (d) V B Q 16. A particle of mass m and charge q is fastened to one end of a string of length l. The other end of the string is fixed to the point O. The whole system lies on a frictionless horizontal plane. Initially, the mass is at rest at A. A uniform electric field in the direction shown is then switched on. Then (a) the speed of the particle when it reaches B is 2qEl m (b) the speed of the particle when it reaches B is qEl m (c) the tension in the string when the particle reaches at B is qE (d) the tension in the string when the particle reaches at B is zero Q 17. A charged particle of mass m and charge q is released from rest from the position (x 0 ,, 0) in a uniform electric field 0 ˆ Ej . The angular momentum of the particle about origin (a) is zero (b) is constant (c) increases with time (d) decreases with time Q 18. A charge + Q is uniformly distributed in a spherical volume of radius R. A particle of charge + q and mass m projected with velocity v 0 from the surface of the spherical volume to its centre inside a smooth tunnel dug across the sphere. The minimum value of v 0 such that it just reaches the centre (assume that there is no resistance on the particle except electrostatic force) of the spherical volume is (a) 0 Qq 2 mR ?? (b) 0 Qq mR ?? (c) 0 2Qq mR ?? (d) 0 Qq 4 mR ?? Page 5 For JEE Advanced Objective Questions Single Correct Option Q 1. In the diagram shown, the charge +Q is fixed. Another charge + 2q and mass M is projected from a distance R from the fixed charge. Minimum separation between the two charges if the velocity becomes 1 3 times of the projected velocity, at this moment is (Assume gravity to be absent) (a) 3 R 2 (b) 1 R 3 (c) 1 R 2 (d) None of these Q 2. A uniform electric field of strength E ? exists in a region. An electron enters a point A with velocity v as shown. It moves through the electric field and reaches at point B. Velocity of particle at B is 2v at 30° with xaxis. Then (a) electric field 2 3mv ˆ Ei 2ea ?? ? (b) rate of doing work done by electric field at B is 3 3mv 2ea (c) Both (a) and (b) are correct (d) Both (a) and (b) are wrong Q 3. Two point charges a and b whose magnitudes are same positioned at a certain distance along the positive xaxis from each other, a is at origin. Graph is drawn between electrical field strength and distance x from a. E is taken positive if it is along the line joining from a to b. From the graph it can be decided that (a) a is positive, b is negative (b) a and b both are positive (c) a and b both are negative (d) a is negative, b is positive Note Graph is drawn only between a and b. Q 4. Six charges are placed at the vertices of a rectangular hexagon as shown in the figure. The electric field on the line passing through point O and perpendicular to the plane of the figure as a function of distance x from point O is (x >>a) (a) 0 (b) 3 0 Qa x ?? (c) 3 0 2Qa x ?? (d) 3 0 3Qa x ?? Q 5. If the electric potential of the inner shell is 10 V and that of the outer shell is 5 V, then the potential at the centre will be (a) 10 V (b) 5 V (c) 15 V (d) zero Q 6. A solid conducting sphere of radius a having a charge q is surrounded by a concentric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure. Find the amount of heat produced when switch is closed 0 1 k 4 ? ?? (a) 2 kq 2a (b) 2 kq 3a (c) 2 kq 4a (d) 2 kq 6a Q 7. There are four concentric shells A,B,C and D of radii a, 2a, 3a and 4a respectively. Shells B and D are given charges + q and  q respectively. Shell C is now earthed. The potential difference V A  V C is 0 1 k 4 ? ?? (a) kq 2a (b) kq 3a (c) kq 4a (d) kq 6a Q 8. Potential difference between centre and surface of the sphere of radius R and uniform volume charge density within it will be (a) 2 0 R 6 ? ? (b) 2 0 R 4 ? ? (c) 2 0 R 3 ? ? (d) 2 0 R 2 ? ? Q 9. A positively charged disc is placed on a horizontal plane. A charged particle is released from a certain height on its axis. The particle just reaches the centre of the disc. Select the correct alternative. (a) Particle has negative charge on it (b) Total potential energy (gravitational + electrostatic) of the particle first increases then decreases (c) Total potential energy of the particle first decreases then increases (d) Total potential energy of the particle continuously decreases Q 10. The curve represents the distribution of potential along the straight line joining the two charges Q 1 and Q 2 (separated by a distance r) then which of the following statements are correct ? 1. Q 1  > Q 2  2. Q 1 is positive in nature 3. A and B are equilibrium points 4. C is a point of unstable equilibrium (a) 1 and 2 (b) 1,2 and 3 (c) 1,2 and 4 (d) 1,2, 3 and 4 Q 11. A point charge q 1 = q is placed at point P. Another point charge q 2 =q is placed at point Q. At some point R(R ? P, R ? Q), electric potential due to q 1 is V 1 and electric potential due to q 2 is V 2 . Which of the following is correct? (a) Only for some points V 1 > V 2 (b) Only for some points V 2 > V 1 (c) For all points V 1 > V 2 (d) For all points V 2 >V 1 Q 12. The variation of electric field between the two charges q 1 and q 2 along the line joining the charges is plotted against distance from q 1 (taking rightward direction of electric field as positive) as shown in the figure. Then the correct statement is (a) q 1 and q 2 are positive and q 1 < q 2 (b) q 1 and q 2 are positive and q 1 > q 2 (c) q 1 is positive and q 2 is negative q 1 <  q 2  (d) q 1 and q 2 are negative and q 1  <  q 2  Q 13. A charge q is placed at O in the cavity in a spherical uncharged conductor. Point S is outside the conductor. If q is displaced from O towards S (still remaining within the cavity) (a) electric field at S will increase (b) electric field at S will decrease (c) electric field at S will first increase and then decrease (d) electric field at S will not change Q 14. A uniform electric field of 400 V/m is directed at 45° above the xaxis as shown in the figure. The potential difference V A  V B is given by (a) 0 (b) 4 V (c) 6.4 V (d) 2.8 V Q 15. Initially the spheres A and B are at potential V A and V B respectively. Now sphere B is earthed by closing the switch. The potential of A will now become (a) 0 (b) V A (c)V A  V B (d) V B Q 16. A particle of mass m and charge q is fastened to one end of a string of length l. The other end of the string is fixed to the point O. The whole system lies on a frictionless horizontal plane. Initially, the mass is at rest at A. A uniform electric field in the direction shown is then switched on. Then (a) the speed of the particle when it reaches B is 2qEl m (b) the speed of the particle when it reaches B is qEl m (c) the tension in the string when the particle reaches at B is qE (d) the tension in the string when the particle reaches at B is zero Q 17. A charged particle of mass m and charge q is released from rest from the position (x 0 ,, 0) in a uniform electric field 0 ˆ Ej . The angular momentum of the particle about origin (a) is zero (b) is constant (c) increases with time (d) decreases with time Q 18. A charge + Q is uniformly distributed in a spherical volume of radius R. A particle of charge + q and mass m projected with velocity v 0 from the surface of the spherical volume to its centre inside a smooth tunnel dug across the sphere. The minimum value of v 0 such that it just reaches the centre (assume that there is no resistance on the particle except electrostatic force) of the spherical volume is (a) 0 Qq 2 mR ?? (b) 0 Qq mR ?? (c) 0 2Qq mR ?? (d) 0 Qq 4 mR ?? Q 19. Two identical coaxial rings each of radius R are separated by a distance of 3R . They are uniformly charged with charges +Q and  Q respectively. The minimum kinetic energy with which a charged particle (charge + q) should be projected from the centre of the negatively charged ring along the axis of the rings such that it reaches the centre of the positively charged ring is (a) 0 Qq 4R ?? (b) 0 Qq 2R ?? (c) 0 Qq 8R ?? (d) 0 3Qq 4R ?? Q 20. A uniform electric field exists in xy plane. The potential of points A (2m, 2m), B(2m, 2m) and C(2m, 4m) are 4 V, 16 V and 12 V respectively. The electric field is (a) ˆˆ (4i 5j)V/ m ? (b) ˆˆ (3i 4j)V/ m ? (c) ˆˆ (3i 4j)V/ m ?? (d) ˆˆ (3i 4j)V/ m ? Q 21. Two fixed charges  2Q and + Q are located at points ( 3a, 0) and (+ 3a, 0) respectively. Then which of the following statement is correct? (a) Points where the electric potential due to the two charges is zero in xy plane, lie on a circle of radius 4a and centre (5a, 0) (b) Potential is zero at x = a and x = 9a (c) Both (a) and (b) are wrong (d) Both (a) and (b) are correct Q 22. A particle of mass m and charge  q is projected from the origin with a horizontal speed v into an electric field of intensity E directed downward. Choose the wrong statement. Neglect gravity (a) The kinetic energy after a displacement y is qEy (b) The horizontal and vertical components of acceleration are a x = 0, a y = qE m (c) The equation of trajectory is 2 2 1 qEx y 2 mv ?? ? ?? ?? (d) The horizontal and vertical displacements x and y after a time t are x = vt and 2 y 1 y a t 2 ? Q 23. A particle of charge  q and mass m moves in a circle of radius r around an infinitely long line charge of linear charge density + ?. Then time period will be where, 0 1 k 4 ? ?? (a) m T 2 r 2k q ?? ? (b) 2 23 4m Tr 2k q ? ? ? (c) 1 2k q T 2 r m ? ? ? (d) 1m T 2 r 2k q ? ??Read More
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