Page 1 1 PHYSICS, CHEMISTRY AND MATHEMATICS Class II IIT-JEE Achiever 2017-2018 Max. Marks 360 Solution to Test - 01 (Integrated) Main Duration Date 3 Hours 15-04-2017 PART I - PHYSICS Multiple choice questions with one correct alternative 1. The figure indicates the electric field lines corresponding to an electric field E. Then (A) E P = E Q = E R (B) E P > E Q > E R (C) E P = E R > E Q (D) E P < E Q < E R Ans (C) Count the number of lines of force 2. There are n electrons of charge e on a drop of oil of density ?. It is in equilibrium (at rest) in an electric field E. The radius of the drop is (A) 1 2 2neE 4 g ? ? ? ? ? ? ? ? (B) 1 2 neE g ? ? ? ? ? ? ? (C) 1 3 3neE 4 g ? ? ? ? ? ? ? ? (D) 1 3 2neE g ? ? ? ? ? ? ? ? Ans (C) 1 3 3 4 3neE mg qE r g neE r 3 4 g ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3. The electric force experienced by a 1 ?C charge is 1.5 ? 10 â€“3 N. the magnitude of the electric field at the position of the charge is (A) 1.5 ? 10 2 NC â€“1 (B) 1.5 ? 10 3 NC â€“1 (C) 1.5 ? 10 4 NC â€“1 (D) 1.5 ? 10 5 NC â€“1 Ans (B) 3 3 1 6 F 1.5 10 F qE E 1.5 10 NC q 1 10 ? ? ? ? ? ? ? ? ? ? ? 4. A water droplet of mass 10 mg and having charge 1.0 ?C stays suspended in a room. The electric field in the room is (A) 10 5 NC â€“1 upwards (B) 10 5 NC â€“1 downwards (C) 10 6 NC â€“1 upwards (D) 10 6 NC â€“1 downwards Ans (A) 3 5 1 6 mg 10 10 10 mg qE E 10 NC q 1.0 10 ? ? ? ? ? ? ? ? ? ? ? 5. A pendulum bob of mass 80 mg, carrying a charge 2 ? 10 â€“8 C is at rest in a uniform horizontal electric field of 20 ? 10 3 NC â€“1 . The tension in the thread is nearly (A) 8 ? 10 â€“4 N (B) 9 ? 10 â€“4 N (C) 8 ? 10 â€“8 N (D) 9 ? 10 â€“8 N Ans (B) 2 2 6 2 8 3 2 4 T (mg) (qE) (80 10 10) (2 10 20 10 ) 9 10 N ? ? ? ? ? ? ? ? ? ? ? ? ? ? P R Q Page 2 1 PHYSICS, CHEMISTRY AND MATHEMATICS Class II IIT-JEE Achiever 2017-2018 Max. Marks 360 Solution to Test - 01 (Integrated) Main Duration Date 3 Hours 15-04-2017 PART I - PHYSICS Multiple choice questions with one correct alternative 1. The figure indicates the electric field lines corresponding to an electric field E. Then (A) E P = E Q = E R (B) E P > E Q > E R (C) E P = E R > E Q (D) E P < E Q < E R Ans (C) Count the number of lines of force 2. There are n electrons of charge e on a drop of oil of density ?. It is in equilibrium (at rest) in an electric field E. The radius of the drop is (A) 1 2 2neE 4 g ? ? ? ? ? ? ? ? (B) 1 2 neE g ? ? ? ? ? ? ? (C) 1 3 3neE 4 g ? ? ? ? ? ? ? ? (D) 1 3 2neE g ? ? ? ? ? ? ? ? Ans (C) 1 3 3 4 3neE mg qE r g neE r 3 4 g ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3. The electric force experienced by a 1 ?C charge is 1.5 ? 10 â€“3 N. the magnitude of the electric field at the position of the charge is (A) 1.5 ? 10 2 NC â€“1 (B) 1.5 ? 10 3 NC â€“1 (C) 1.5 ? 10 4 NC â€“1 (D) 1.5 ? 10 5 NC â€“1 Ans (B) 3 3 1 6 F 1.5 10 F qE E 1.5 10 NC q 1 10 ? ? ? ? ? ? ? ? ? ? ? 4. A water droplet of mass 10 mg and having charge 1.0 ?C stays suspended in a room. The electric field in the room is (A) 10 5 NC â€“1 upwards (B) 10 5 NC â€“1 downwards (C) 10 6 NC â€“1 upwards (D) 10 6 NC â€“1 downwards Ans (A) 3 5 1 6 mg 10 10 10 mg qE E 10 NC q 1.0 10 ? ? ? ? ? ? ? ? ? ? ? 5. A pendulum bob of mass 80 mg, carrying a charge 2 ? 10 â€“8 C is at rest in a uniform horizontal electric field of 20 ? 10 3 NC â€“1 . The tension in the thread is nearly (A) 8 ? 10 â€“4 N (B) 9 ? 10 â€“4 N (C) 8 ? 10 â€“8 N (D) 9 ? 10 â€“8 N Ans (B) 2 2 6 2 8 3 2 4 T (mg) (qE) (80 10 10) (2 10 20 10 ) 9 10 N ? ? ? ? ? ? ? ? ? ? ? ? ? ? P R Q 2IIT1718PCMT1SM(Intg) 2 6. Consider a uniformly charged ring of radius R. The point on the axis of the ring where the electric field is maximum is at a distance x from the centre of the ring. The value of x is (A) R 2 (B) R 3 (C) R 3 (D) R 2 Ans (D) 7. A circular wire loop of radius R carries a total charge Q distributed uniformly over its length. A small length dl of the wire is cut off. The electric field at the centre due to the remaining wire is (A) 2 3 0 Q(d ) 8 R ? ? l (B) 3 0 Q(d ) 4 R ? ? l (C) 2 3 0 Q(d ) 4 R ? ? l (D) 3 0 Q(d ) 8 R ? ? l Ans (A) The electric field due to the remaining wire is equal and opposite to the field produced by the charge element dl. ? 2 2 2 3 0 0 0 1 d 1 Q d Q(d ) E 4 R 4 2 R R 8 R ? ? ? ? ? ? ? ? ? ? ? l l l 8. A wire of length l with a uniform charge density ? is bent in the form of a regular hexagon. The electric field at the centre of the hexagon is (A) 0 4 ? ? ? l (B) 0 2 ? ? ? l (C) 0 8 ? ? ? l (D) zero Ans (D) 9. A charged particle of mass m = 2 kg and charge 1 ?C is projected from a horizontal ground at an angle ? = 45 ? with speed 10 ms â€“1 . In space, a horizontal electric field toward the direction of projection E = 2 ? 10 7 NC â€“1 exists. The range of the projectile is (A) 20 m (B) 60 m (C) 200 m (D) 180 m Ans (A) 6 7 2 x qE 10 2 10 a 10 ms m 2 ? ? ? ? ? ? ? Time of flight 1 2 10 2usin 2 T 2 s g 10 ? ? ? ? ? ? Hence, 2 x x 1 R u T a T 2 ? ? 2 x 1 10cos45 T a T 2 ? ? ? ? 10 1 2 10 2 2 2 ? ? ? ? ? = 20 m 10. Three positive point charges q 1 , q 2 and q 3 form an isolated system. Suppose the charges have generated a property due to which like charges also attract. The charges are moving along a circle with same speed maintaining angles as shown in the figure. The charge q 1 experiences a force f 1 due to other two charges. Similarly, q 2 experiences a force f 2 and q 3 , a force f 3 . The ratio f 1 : f 2 : f 3 is (A) 1 : 1 : 1 (B) q 1 : q 2 : q 3 (C) 1 : 3 : 2 (D) this ratio cannot be calculated Ans (C) Page 3 1 PHYSICS, CHEMISTRY AND MATHEMATICS Class II IIT-JEE Achiever 2017-2018 Max. Marks 360 Solution to Test - 01 (Integrated) Main Duration Date 3 Hours 15-04-2017 PART I - PHYSICS Multiple choice questions with one correct alternative 1. The figure indicates the electric field lines corresponding to an electric field E. Then (A) E P = E Q = E R (B) E P > E Q > E R (C) E P = E R > E Q (D) E P < E Q < E R Ans (C) Count the number of lines of force 2. There are n electrons of charge e on a drop of oil of density ?. It is in equilibrium (at rest) in an electric field E. The radius of the drop is (A) 1 2 2neE 4 g ? ? ? ? ? ? ? ? (B) 1 2 neE g ? ? ? ? ? ? ? (C) 1 3 3neE 4 g ? ? ? ? ? ? ? ? (D) 1 3 2neE g ? ? ? ? ? ? ? ? Ans (C) 1 3 3 4 3neE mg qE r g neE r 3 4 g ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3. The electric force experienced by a 1 ?C charge is 1.5 ? 10 â€“3 N. the magnitude of the electric field at the position of the charge is (A) 1.5 ? 10 2 NC â€“1 (B) 1.5 ? 10 3 NC â€“1 (C) 1.5 ? 10 4 NC â€“1 (D) 1.5 ? 10 5 NC â€“1 Ans (B) 3 3 1 6 F 1.5 10 F qE E 1.5 10 NC q 1 10 ? ? ? ? ? ? ? ? ? ? ? 4. A water droplet of mass 10 mg and having charge 1.0 ?C stays suspended in a room. The electric field in the room is (A) 10 5 NC â€“1 upwards (B) 10 5 NC â€“1 downwards (C) 10 6 NC â€“1 upwards (D) 10 6 NC â€“1 downwards Ans (A) 3 5 1 6 mg 10 10 10 mg qE E 10 NC q 1.0 10 ? ? ? ? ? ? ? ? ? ? ? 5. A pendulum bob of mass 80 mg, carrying a charge 2 ? 10 â€“8 C is at rest in a uniform horizontal electric field of 20 ? 10 3 NC â€“1 . The tension in the thread is nearly (A) 8 ? 10 â€“4 N (B) 9 ? 10 â€“4 N (C) 8 ? 10 â€“8 N (D) 9 ? 10 â€“8 N Ans (B) 2 2 6 2 8 3 2 4 T (mg) (qE) (80 10 10) (2 10 20 10 ) 9 10 N ? ? ? ? ? ? ? ? ? ? ? ? ? ? P R Q 2IIT1718PCMT1SM(Intg) 2 6. Consider a uniformly charged ring of radius R. The point on the axis of the ring where the electric field is maximum is at a distance x from the centre of the ring. The value of x is (A) R 2 (B) R 3 (C) R 3 (D) R 2 Ans (D) 7. A circular wire loop of radius R carries a total charge Q distributed uniformly over its length. A small length dl of the wire is cut off. The electric field at the centre due to the remaining wire is (A) 2 3 0 Q(d ) 8 R ? ? l (B) 3 0 Q(d ) 4 R ? ? l (C) 2 3 0 Q(d ) 4 R ? ? l (D) 3 0 Q(d ) 8 R ? ? l Ans (A) The electric field due to the remaining wire is equal and opposite to the field produced by the charge element dl. ? 2 2 2 3 0 0 0 1 d 1 Q d Q(d ) E 4 R 4 2 R R 8 R ? ? ? ? ? ? ? ? ? ? ? l l l 8. A wire of length l with a uniform charge density ? is bent in the form of a regular hexagon. The electric field at the centre of the hexagon is (A) 0 4 ? ? ? l (B) 0 2 ? ? ? l (C) 0 8 ? ? ? l (D) zero Ans (D) 9. A charged particle of mass m = 2 kg and charge 1 ?C is projected from a horizontal ground at an angle ? = 45 ? with speed 10 ms â€“1 . In space, a horizontal electric field toward the direction of projection E = 2 ? 10 7 NC â€“1 exists. The range of the projectile is (A) 20 m (B) 60 m (C) 200 m (D) 180 m Ans (A) 6 7 2 x qE 10 2 10 a 10 ms m 2 ? ? ? ? ? ? ? Time of flight 1 2 10 2usin 2 T 2 s g 10 ? ? ? ? ? ? Hence, 2 x x 1 R u T a T 2 ? ? 2 x 1 10cos45 T a T 2 ? ? ? ? 10 1 2 10 2 2 2 ? ? ? ? ? = 20 m 10. Three positive point charges q 1 , q 2 and q 3 form an isolated system. Suppose the charges have generated a property due to which like charges also attract. The charges are moving along a circle with same speed maintaining angles as shown in the figure. The charge q 1 experiences a force f 1 due to other two charges. Similarly, q 2 experiences a force f 2 and q 3 , a force f 3 . The ratio f 1 : f 2 : f 3 is (A) 1 : 1 : 1 (B) q 1 : q 2 : q 3 (C) 1 : 3 : 2 (D) this ratio cannot be calculated Ans (C) 3 Since the charges exert force on one another that are in action-reaction pair, sum of forces 1 2 3 f , f and f ? ? ? is zero. So force vectors form a triangle, as shown in the figure. Applying sine rule, we have 3 1 2 f f f sin30 sin 60 sin90 ? ? or 2 1 3 2f 2f f K (sup pose) 3 ? ? ? 1 2 3 k 3 f , f K, f K 2 2 ? ? ? So, 1 2 3 1 3 f : f : f : : 1 1 : 3 : 2 2 2 ? ? 11. Two mutually perpendicular wire carry charge densities ? 1 and ? 2 . The electric lines of force makes angle ? with second wire, then 1 2 ? ? is (A) tan 2 ? (B) cot 2 ? (C) sin 2 ? (D) cos 2 ? Ans (B) 1 1 0 E 2 x ? ? ? ? and 2 2 0 E 2 y ? ? ? ? 1 1 2 2 E y E x ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1 2 1 tan tan ? ? ? ? ? ? ? ? ? ? ? or 2 1 2 cot ? ? ? ? 12. A non-conducting ring of mass m and radius R is charged as shown. The magnitude of charge density, (i.e., charge per unit length) is ?. It is then placed on a smooth non-conducting horizontal plane. At time t = 0, a uniform electric field 0 Ë† E E i ? ? is switched on. The angular acceleration of the ring at that instant is: (A) 0 2 E m ? (B) 0 E m ? (C) 0 2 E 3m ? (D) none of these Ans (B) Consider an infinitesimal element subtending an angle d ? at the centre and at angle ? as shown in figure. dF = ?Rd ?E 0 A force of same magnitude but in opposite direction acts on a corresponding element in the region of negative charge. Net torque due to both types of charges is d ? = ( ?Rd ?E 0 ) (2Rsin ?) ? 2 2 0 0 2 R E sin d ? ? ? ? ? ? ? ? 2 0 2 R E ? ? ? Equation for pure rolling motion is ? ? = I ? ? 2 ?R 2 E 0 = mR 2 ? y x E 0 + + + ? ? ? ? Page 4 1 PHYSICS, CHEMISTRY AND MATHEMATICS Class II IIT-JEE Achiever 2017-2018 Max. Marks 360 Solution to Test - 01 (Integrated) Main Duration Date 3 Hours 15-04-2017 PART I - PHYSICS Multiple choice questions with one correct alternative 1. The figure indicates the electric field lines corresponding to an electric field E. Then (A) E P = E Q = E R (B) E P > E Q > E R (C) E P = E R > E Q (D) E P < E Q < E R Ans (C) Count the number of lines of force 2. There are n electrons of charge e on a drop of oil of density ?. It is in equilibrium (at rest) in an electric field E. The radius of the drop is (A) 1 2 2neE 4 g ? ? ? ? ? ? ? ? (B) 1 2 neE g ? ? ? ? ? ? ? (C) 1 3 3neE 4 g ? ? ? ? ? ? ? ? (D) 1 3 2neE g ? ? ? ? ? ? ? ? Ans (C) 1 3 3 4 3neE mg qE r g neE r 3 4 g ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3. The electric force experienced by a 1 ?C charge is 1.5 ? 10 â€“3 N. the magnitude of the electric field at the position of the charge is (A) 1.5 ? 10 2 NC â€“1 (B) 1.5 ? 10 3 NC â€“1 (C) 1.5 ? 10 4 NC â€“1 (D) 1.5 ? 10 5 NC â€“1 Ans (B) 3 3 1 6 F 1.5 10 F qE E 1.5 10 NC q 1 10 ? ? ? ? ? ? ? ? ? ? ? 4. A water droplet of mass 10 mg and having charge 1.0 ?C stays suspended in a room. The electric field in the room is (A) 10 5 NC â€“1 upwards (B) 10 5 NC â€“1 downwards (C) 10 6 NC â€“1 upwards (D) 10 6 NC â€“1 downwards Ans (A) 3 5 1 6 mg 10 10 10 mg qE E 10 NC q 1.0 10 ? ? ? ? ? ? ? ? ? ? ? 5. A pendulum bob of mass 80 mg, carrying a charge 2 ? 10 â€“8 C is at rest in a uniform horizontal electric field of 20 ? 10 3 NC â€“1 . The tension in the thread is nearly (A) 8 ? 10 â€“4 N (B) 9 ? 10 â€“4 N (C) 8 ? 10 â€“8 N (D) 9 ? 10 â€“8 N Ans (B) 2 2 6 2 8 3 2 4 T (mg) (qE) (80 10 10) (2 10 20 10 ) 9 10 N ? ? ? ? ? ? ? ? ? ? ? ? ? ? P R Q 2IIT1718PCMT1SM(Intg) 2 6. Consider a uniformly charged ring of radius R. The point on the axis of the ring where the electric field is maximum is at a distance x from the centre of the ring. The value of x is (A) R 2 (B) R 3 (C) R 3 (D) R 2 Ans (D) 7. A circular wire loop of radius R carries a total charge Q distributed uniformly over its length. A small length dl of the wire is cut off. The electric field at the centre due to the remaining wire is (A) 2 3 0 Q(d ) 8 R ? ? l (B) 3 0 Q(d ) 4 R ? ? l (C) 2 3 0 Q(d ) 4 R ? ? l (D) 3 0 Q(d ) 8 R ? ? l Ans (A) The electric field due to the remaining wire is equal and opposite to the field produced by the charge element dl. ? 2 2 2 3 0 0 0 1 d 1 Q d Q(d ) E 4 R 4 2 R R 8 R ? ? ? ? ? ? ? ? ? ? ? l l l 8. A wire of length l with a uniform charge density ? is bent in the form of a regular hexagon. The electric field at the centre of the hexagon is (A) 0 4 ? ? ? l (B) 0 2 ? ? ? l (C) 0 8 ? ? ? l (D) zero Ans (D) 9. A charged particle of mass m = 2 kg and charge 1 ?C is projected from a horizontal ground at an angle ? = 45 ? with speed 10 ms â€“1 . In space, a horizontal electric field toward the direction of projection E = 2 ? 10 7 NC â€“1 exists. The range of the projectile is (A) 20 m (B) 60 m (C) 200 m (D) 180 m Ans (A) 6 7 2 x qE 10 2 10 a 10 ms m 2 ? ? ? ? ? ? ? Time of flight 1 2 10 2usin 2 T 2 s g 10 ? ? ? ? ? ? Hence, 2 x x 1 R u T a T 2 ? ? 2 x 1 10cos45 T a T 2 ? ? ? ? 10 1 2 10 2 2 2 ? ? ? ? ? = 20 m 10. Three positive point charges q 1 , q 2 and q 3 form an isolated system. Suppose the charges have generated a property due to which like charges also attract. The charges are moving along a circle with same speed maintaining angles as shown in the figure. The charge q 1 experiences a force f 1 due to other two charges. Similarly, q 2 experiences a force f 2 and q 3 , a force f 3 . The ratio f 1 : f 2 : f 3 is (A) 1 : 1 : 1 (B) q 1 : q 2 : q 3 (C) 1 : 3 : 2 (D) this ratio cannot be calculated Ans (C) 3 Since the charges exert force on one another that are in action-reaction pair, sum of forces 1 2 3 f , f and f ? ? ? is zero. So force vectors form a triangle, as shown in the figure. Applying sine rule, we have 3 1 2 f f f sin30 sin 60 sin90 ? ? or 2 1 3 2f 2f f K (sup pose) 3 ? ? ? 1 2 3 k 3 f , f K, f K 2 2 ? ? ? So, 1 2 3 1 3 f : f : f : : 1 1 : 3 : 2 2 2 ? ? 11. Two mutually perpendicular wire carry charge densities ? 1 and ? 2 . The electric lines of force makes angle ? with second wire, then 1 2 ? ? is (A) tan 2 ? (B) cot 2 ? (C) sin 2 ? (D) cos 2 ? Ans (B) 1 1 0 E 2 x ? ? ? ? and 2 2 0 E 2 y ? ? ? ? 1 1 2 2 E y E x ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1 2 1 tan tan ? ? ? ? ? ? ? ? ? ? ? or 2 1 2 cot ? ? ? ? 12. A non-conducting ring of mass m and radius R is charged as shown. The magnitude of charge density, (i.e., charge per unit length) is ?. It is then placed on a smooth non-conducting horizontal plane. At time t = 0, a uniform electric field 0 Ë† E E i ? ? is switched on. The angular acceleration of the ring at that instant is: (A) 0 2 E m ? (B) 0 E m ? (C) 0 2 E 3m ? (D) none of these Ans (B) Consider an infinitesimal element subtending an angle d ? at the centre and at angle ? as shown in figure. dF = ?Rd ?E 0 A force of same magnitude but in opposite direction acts on a corresponding element in the region of negative charge. Net torque due to both types of charges is d ? = ( ?Rd ?E 0 ) (2Rsin ?) ? 2 2 0 0 2 R E sin d ? ? ? ? ? ? ? ? 2 0 2 R E ? ? ? Equation for pure rolling motion is ? ? = I ? ? 2 ?R 2 E 0 = mR 2 ? y x E 0 + + + ? ? ? ? 2IIT1718PCMT1SM(Intg) 4 13. A positively charged thin metal ring of radius R is fixed in the x-y plane with its centre at the origin O. A negatively charged particle is released from rest at the point (0, 0, z 0 ) where z 0 > 0. Then the motion of P is (A) periodic, for all values of z 0 satisfying 0 < z 0 < ?. (B) simple harmonic, for all the values of z 0 satisfying 0 < z 0 ? R. (C) approximately simple harmonic for all values of z 0 . (D) such that crosses O and continues to move along the negative z-axis. Ans (A) Here electric field; E = ? ? 0 3 2 2 2 0 0 Qz 4 R z ? ? ? where Q is charge on the ring and z 0 is the axial point distance from O. Then F = qE = ? ? 0 3 2 2 2 0 0 Qqz 4 R z ? ? ? When charge ( ?q) crosses origin, force is again towards the centre; i.e. motion is periodic. Now for z 0 << R; F = 0 3 0 Qqz 4 R ? ? where clearly F is proportional to the displacement z 0 from the mean position. ? Motion is SHM only for z 0 << R . 14. Two point charges a b q and q whose strengths are equal in magnitude are positioned at a certain distance from each other. Assuming the field strength is positive in the direction coinciding with the positive direction of x-axis, determine the signs of charges for the distribution of the field strength between the charges shown in figure. (A) q a ? + ve, q b ? ?ve (B) q a ? ?ve, q b ? + ve (C) q a ? + ve, q b ? + ve (D) q a ? ?ve, q b ? ?ve Ans (A) This problem is related to the graphical representation of electric field due to a system of charges. To the right of q a field is + ve. So q a is + ve. To the left of q b field is + ve so q b is ?ve. 15. Two positive point charges q are placed on the x-axis, one at x = a and another at x = -a on the x-axis. The graph of the x-component of the electric field as a function of x, for values of x between -4a and +4a is correctly shown in (A) (B) (C) (D) Ans (A) Check the direction of electric field at a point and then trace the graph E x a a x E x a a E x a a x a a E x Page 5 1 PHYSICS, CHEMISTRY AND MATHEMATICS Class II IIT-JEE Achiever 2017-2018 Max. Marks 360 Solution to Test - 01 (Integrated) Main Duration Date 3 Hours 15-04-2017 PART I - PHYSICS Multiple choice questions with one correct alternative 1. The figure indicates the electric field lines corresponding to an electric field E. Then (A) E P = E Q = E R (B) E P > E Q > E R (C) E P = E R > E Q (D) E P < E Q < E R Ans (C) Count the number of lines of force 2. There are n electrons of charge e on a drop of oil of density ?. It is in equilibrium (at rest) in an electric field E. The radius of the drop is (A) 1 2 2neE 4 g ? ? ? ? ? ? ? ? (B) 1 2 neE g ? ? ? ? ? ? ? (C) 1 3 3neE 4 g ? ? ? ? ? ? ? ? (D) 1 3 2neE g ? ? ? ? ? ? ? ? Ans (C) 1 3 3 4 3neE mg qE r g neE r 3 4 g ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 3. The electric force experienced by a 1 ?C charge is 1.5 ? 10 â€“3 N. the magnitude of the electric field at the position of the charge is (A) 1.5 ? 10 2 NC â€“1 (B) 1.5 ? 10 3 NC â€“1 (C) 1.5 ? 10 4 NC â€“1 (D) 1.5 ? 10 5 NC â€“1 Ans (B) 3 3 1 6 F 1.5 10 F qE E 1.5 10 NC q 1 10 ? ? ? ? ? ? ? ? ? ? ? 4. A water droplet of mass 10 mg and having charge 1.0 ?C stays suspended in a room. The electric field in the room is (A) 10 5 NC â€“1 upwards (B) 10 5 NC â€“1 downwards (C) 10 6 NC â€“1 upwards (D) 10 6 NC â€“1 downwards Ans (A) 3 5 1 6 mg 10 10 10 mg qE E 10 NC q 1.0 10 ? ? ? ? ? ? ? ? ? ? ? 5. A pendulum bob of mass 80 mg, carrying a charge 2 ? 10 â€“8 C is at rest in a uniform horizontal electric field of 20 ? 10 3 NC â€“1 . The tension in the thread is nearly (A) 8 ? 10 â€“4 N (B) 9 ? 10 â€“4 N (C) 8 ? 10 â€“8 N (D) 9 ? 10 â€“8 N Ans (B) 2 2 6 2 8 3 2 4 T (mg) (qE) (80 10 10) (2 10 20 10 ) 9 10 N ? ? ? ? ? ? ? ? ? ? ? ? ? ? P R Q 2IIT1718PCMT1SM(Intg) 2 6. Consider a uniformly charged ring of radius R. The point on the axis of the ring where the electric field is maximum is at a distance x from the centre of the ring. The value of x is (A) R 2 (B) R 3 (C) R 3 (D) R 2 Ans (D) 7. A circular wire loop of radius R carries a total charge Q distributed uniformly over its length. A small length dl of the wire is cut off. The electric field at the centre due to the remaining wire is (A) 2 3 0 Q(d ) 8 R ? ? l (B) 3 0 Q(d ) 4 R ? ? l (C) 2 3 0 Q(d ) 4 R ? ? l (D) 3 0 Q(d ) 8 R ? ? l Ans (A) The electric field due to the remaining wire is equal and opposite to the field produced by the charge element dl. ? 2 2 2 3 0 0 0 1 d 1 Q d Q(d ) E 4 R 4 2 R R 8 R ? ? ? ? ? ? ? ? ? ? ? l l l 8. A wire of length l with a uniform charge density ? is bent in the form of a regular hexagon. The electric field at the centre of the hexagon is (A) 0 4 ? ? ? l (B) 0 2 ? ? ? l (C) 0 8 ? ? ? l (D) zero Ans (D) 9. A charged particle of mass m = 2 kg and charge 1 ?C is projected from a horizontal ground at an angle ? = 45 ? with speed 10 ms â€“1 . In space, a horizontal electric field toward the direction of projection E = 2 ? 10 7 NC â€“1 exists. The range of the projectile is (A) 20 m (B) 60 m (C) 200 m (D) 180 m Ans (A) 6 7 2 x qE 10 2 10 a 10 ms m 2 ? ? ? ? ? ? ? Time of flight 1 2 10 2usin 2 T 2 s g 10 ? ? ? ? ? ? Hence, 2 x x 1 R u T a T 2 ? ? 2 x 1 10cos45 T a T 2 ? ? ? ? 10 1 2 10 2 2 2 ? ? ? ? ? = 20 m 10. Three positive point charges q 1 , q 2 and q 3 form an isolated system. Suppose the charges have generated a property due to which like charges also attract. The charges are moving along a circle with same speed maintaining angles as shown in the figure. The charge q 1 experiences a force f 1 due to other two charges. Similarly, q 2 experiences a force f 2 and q 3 , a force f 3 . The ratio f 1 : f 2 : f 3 is (A) 1 : 1 : 1 (B) q 1 : q 2 : q 3 (C) 1 : 3 : 2 (D) this ratio cannot be calculated Ans (C) 3 Since the charges exert force on one another that are in action-reaction pair, sum of forces 1 2 3 f , f and f ? ? ? is zero. So force vectors form a triangle, as shown in the figure. Applying sine rule, we have 3 1 2 f f f sin30 sin 60 sin90 ? ? or 2 1 3 2f 2f f K (sup pose) 3 ? ? ? 1 2 3 k 3 f , f K, f K 2 2 ? ? ? So, 1 2 3 1 3 f : f : f : : 1 1 : 3 : 2 2 2 ? ? 11. Two mutually perpendicular wire carry charge densities ? 1 and ? 2 . The electric lines of force makes angle ? with second wire, then 1 2 ? ? is (A) tan 2 ? (B) cot 2 ? (C) sin 2 ? (D) cos 2 ? Ans (B) 1 1 0 E 2 x ? ? ? ? and 2 2 0 E 2 y ? ? ? ? 1 1 2 2 E y E x ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1 2 1 tan tan ? ? ? ? ? ? ? ? ? ? ? or 2 1 2 cot ? ? ? ? 12. A non-conducting ring of mass m and radius R is charged as shown. The magnitude of charge density, (i.e., charge per unit length) is ?. It is then placed on a smooth non-conducting horizontal plane. At time t = 0, a uniform electric field 0 Ë† E E i ? ? is switched on. The angular acceleration of the ring at that instant is: (A) 0 2 E m ? (B) 0 E m ? (C) 0 2 E 3m ? (D) none of these Ans (B) Consider an infinitesimal element subtending an angle d ? at the centre and at angle ? as shown in figure. dF = ?Rd ?E 0 A force of same magnitude but in opposite direction acts on a corresponding element in the region of negative charge. Net torque due to both types of charges is d ? = ( ?Rd ?E 0 ) (2Rsin ?) ? 2 2 0 0 2 R E sin d ? ? ? ? ? ? ? ? 2 0 2 R E ? ? ? Equation for pure rolling motion is ? ? = I ? ? 2 ?R 2 E 0 = mR 2 ? y x E 0 + + + ? ? ? ? 2IIT1718PCMT1SM(Intg) 4 13. A positively charged thin metal ring of radius R is fixed in the x-y plane with its centre at the origin O. A negatively charged particle is released from rest at the point (0, 0, z 0 ) where z 0 > 0. Then the motion of P is (A) periodic, for all values of z 0 satisfying 0 < z 0 < ?. (B) simple harmonic, for all the values of z 0 satisfying 0 < z 0 ? R. (C) approximately simple harmonic for all values of z 0 . (D) such that crosses O and continues to move along the negative z-axis. Ans (A) Here electric field; E = ? ? 0 3 2 2 2 0 0 Qz 4 R z ? ? ? where Q is charge on the ring and z 0 is the axial point distance from O. Then F = qE = ? ? 0 3 2 2 2 0 0 Qqz 4 R z ? ? ? When charge ( ?q) crosses origin, force is again towards the centre; i.e. motion is periodic. Now for z 0 << R; F = 0 3 0 Qqz 4 R ? ? where clearly F is proportional to the displacement z 0 from the mean position. ? Motion is SHM only for z 0 << R . 14. Two point charges a b q and q whose strengths are equal in magnitude are positioned at a certain distance from each other. Assuming the field strength is positive in the direction coinciding with the positive direction of x-axis, determine the signs of charges for the distribution of the field strength between the charges shown in figure. (A) q a ? + ve, q b ? ?ve (B) q a ? ?ve, q b ? + ve (C) q a ? + ve, q b ? + ve (D) q a ? ?ve, q b ? ?ve Ans (A) This problem is related to the graphical representation of electric field due to a system of charges. To the right of q a field is + ve. So q a is + ve. To the left of q b field is + ve so q b is ?ve. 15. Two positive point charges q are placed on the x-axis, one at x = a and another at x = -a on the x-axis. The graph of the x-component of the electric field as a function of x, for values of x between -4a and +4a is correctly shown in (A) (B) (C) (D) Ans (A) Check the direction of electric field at a point and then trace the graph E x a a x E x a a E x a a x a a E x 5 16. The dielectric constant K of an insulator cannot be (A) 4 (B) 6 (C) ? (D) 9 Ans (C) K can have all values lying between zero (for perfect insulator) to infinity (for perfect conductor) option (C) is correct. 17. A force F acts between sodium and chlorine ions of salt [sodium chloride] when put 1 cm apart in air. The permittivity of air and dielectric constant of water are ? 0 and K, respectively. When a piece of salt is put in water, electrical force acting between sodium and chlorine ions 1 cm apart is (A) F (B) 0 FK ? (C) F K (D) 0 F K ? Ans (C) 2 0 e e F ,in air 4 r ? ? ? ? 2 0 e e F , in medium 4 Kr ? ? ? ? ? F F K ? ? 18. The charge contained in 500 cc of water due to protons will be (A) 6.0 ? 10 27 C (B) 2.67 ? 10 7 C (C) 6 ? 10 23 C (D) 1.67 ? 10 23 C Ans (B) No. of H 2 O molecules in 500 cc. 23 Av mass N 500 6 10 Mol.wt 18 ? ? ? ? ? Each molecule contains 10 protons 23 19 7 10 500 q 6 10 1.6 10 coul 2.67 10 C 18 ? ? ? ? ? ? ? ? ? ? 19. Two identical copper spheres are separated by 1 m in vacuum. The number of electrons that have to be removed from one sphere and added to the other so that they attract each other with a force of 0.9 N is (A) 6.25 ? 10 15 (B) 42.5 ? 10 15 (C) 6.25 ? 10 13 (D) 42.5 ? 10 13 Ans (C) 1 2 1 2 2 0 1 q q F , q q ne 4 r ? ? ? ? ? (n ? No. of electrons removed/added) 20. Two charges 2C and 6C are separated by a finite distance. The force between them is 12 ? 10 3 N. If a charge ?4C is added to each of them, the force now becomes (A) 4 ? 10 3 N repulsion (B) 4 ? 10 2 N repulsion (C) 6 ? 10 3 N attraction (D) 4 ? 10 3 N attraction Ans (D) 1 2 1 2 1 1 2 F q q F q q , , q 2C 4C 2C F q q ? ? ? ? ? ? ? ? ? ? 2 q 6C 4C 2C ? ? ? ?Read More

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