* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download MODULE :2 Lecture 6 Multiple Choice Questions : 1. Eight
Survey
Document related concepts
Weightlessness wikipedia , lookup
Standard Model wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Newton's theorem of revolving orbits wikipedia , lookup
AharonovβBohm effect wikipedia , lookup
Electromagnetism wikipedia , lookup
Field (physics) wikipedia , lookup
Speed of gravity wikipedia , lookup
Anti-gravity wikipedia , lookup
Maxwell's equations wikipedia , lookup
Elementary particle wikipedia , lookup
Magnetic monopole wikipedia , lookup
Fundamental interaction wikipedia , lookup
Work (physics) wikipedia , lookup
Centripetal force wikipedia , lookup
Lorentz force wikipedia , lookup
Transcript
MODULE :2 Lecture 6 Multiple Choice Questions : 1. Eight charges, each +q, are located symmetrically on a circle of radius R with P as its centre. If the charge at the position X is removed and brought to the location P, the force on this charge will be a. b. c. d. 1 ππ 2 from X to P 4ππππ π π 2 7 ππ 2 from X to P 4ππππ π π 2 1 ππ 2 4ππππ π π 2 7 ππ 2 4ππππ π π 2 X from P to X P from P to X 2. Twelve charges are positioned on the dial of a wall clock such that a charge Q is at the position 1, 2Q at position 2, 3Q at 3 and so on, ending with 12Q at the position 12. If O is at the centre of the dial, what is the force exerted on a unit charge located at O, assuming the radius of the dial to be of unit length? y a. οΏ½12 + 6β3οΏ½ππΜ + 6ππΜ b. βοΏ½12 + 6β3οΏ½ππΜ + 6ππΜ c. οΏ½12 + 6β3οΏ½ππΜ β 6ππΜ d. βοΏ½12 + 6β3οΏ½ππΜ β 6ππΜ x 3. Two small conducting spheres attract each other electrostatically. It can be concluded that a. At least one of the spheres is charged b. Both the spheres are charged c. Both the spheres are charged and their charges are of opposite sign 4. 5. 6. 7. 8. d. No definite conclusion on their charge state can be made from the given data. Electric field lines are a. Vectors in the direction of the electric force that acts on a test charge b. Trajectories of a test charge in the electric field c. Closed loops d. Pictorial representation of electric field around a charged object. The total amount of negative charge of all the electrons contained in one mole of water is approximately a. 1C b. 105 C c. 106C d. 1023C A negative charge of 9µC and mass 2µkg orbits around a heavy positive charge of 16µC in a circular orbit of radius 5m. What is the speed of the negative charge? a. 180 m/s b. 324 m/s c. 360 m/s d. 1984 m/s A 2.5 µC test charge is placed to the right of another charge Q. If there is an attractive force of 22.5 N between the two, what would be the force exerted if the magnitude of the test charge were to be doubled but it stayed at the same location as before? a. 90 N b. 45 N c. 11.25 N d. Depends on the distance between the test charge and the charge Q. The charges ππ, ππ, β4ππand β ππ are kept at the corners A, B, C and D , respectively, of a square. If the force between the charges at A and B is F, the net force exerted on the charge at A due to the other three charges is a. b. c. d. e. 6F 3πΉπΉ β6πΉπΉ β3πΉπΉ A B D C 9. Two small conducting spheres of mass m and charge q each are suspended from a common point by means of threads. The spheres settle down to an equilibrium position, each making an angle ΞΈ with the vertical. The tension in either of the threads is a. b. c. d. Zero Greater than mg Less than mg Equal to mg 10. Two opposite charges are placed on the paper, as shown in the figure. The charge on the left is three times as big as the charge on the right. Other than at infinity, where else can the force on a unit test charge due to these two charges is zero? d a. b. c. d. To the right of the smaller charge Between the two charges To the left of the bigger charge Depends on the sign of the test charge Answers to Multiple Choice Questions 1. (b) 2. (c) 3. (a) 4. (d) 5. (c) 6. (c) 7. (b) 8. (c) 9. (b) 10. (a) Problems : 1. ABC is an equilateral triangle of side 40 cm. At the vertices A and B +4µC of charge is kept fixed while at the vertex C a β4ππC charge is held. What is the force on the charge at C? If now, the charge at C is released while the charges at A and B still remain fixed, describe its subsequent motion. A C B 2. Two equal and positive charges, q each, are at a finite distance 2d from each other. A third charge Q is located at the midpoint of the line joining the two. Where should a unit positive charge be placed so that the net force on it zero? What, if any, is the requirement of the magnitude and sign of the charge Q? 3. Twelve equal charges +q are situated on a circle of radius R and they are equally spaced like the position of digits on the dial of a clock. What is the net force on a charge Q kept at the centre? What would be the force on Q if the charge at 3βo clock position is removed? 4. Two particles, each of mass m and having charges q and 2q are suspended by strings of length l from a common point. Find the angle ΞΈ that each string makes with the vertical. 5. A particle of mass m and with charge q is suspended from a peg on a wall by means of a string of length 0.5m. The string makes an angle 600 with the vertical. Another charge q is held at the same horizontal level as the first charge so that the distance between the charges is R. Calculate the tension in the string and the distance R. 6. A wire is bent in the form of a semicircle and carries a linear charge density Ξ». Find the electric field at the centre of the circle. Hints for solutions to problems : 1. Resolve the forces along the perpendicular bisector from C on to AB and a direction perpendicular to it. The net force is along the perpendicular bisector towards AB and has a magnitude 1.56 N. 2. Charge Q has to have opposite sign of the charge q; else at no finite distance field can be zero. In order that forces cancel out, the test charge must be located along the perpendicular at Q of the line joining the two charges q. q Q q ΞΈ P Resolve the forces due to the pair q, the components perpendicular to QP cancel. Along QP, it has to be canceled by the repulsive force due to Q. The condition gives cos3 ππ = ππ/2ππ. 3. When equal charges are kept on the dial, the net force on a charge at the centre is zero as the forces due to a pair kept in diametrically opposite positions cancel. If a single charge is removed, the effect is due to the diametrically opposite member. 4. Draw the freebody diagram of each particle. Resole forces along vertical and horizontal. Fe π»π» ππππππ π½π½ = ππππ π»π» π¬π¬π¬π¬π¬π¬ π½π½ = ππ ΞΈ T 2q q mg ππππππ ππππππππ ππππππ ππππππππ π½π½ Eliminate T to get the angle ΞΈ. 5. Very similar to Problem 4. The right hand side of the second equation is to be changed to ππ ππππ ππππππππ πΉπΉππ . Since the angle is given and T can be eliminated, one can find R. 6. Consider the field at P due to an element RdΞΈ located at an angle ΞΈ, as shown. The magnitude of the field due to this element is given by ππππ = 1 4ππππ 0 ππππ ππππ π π 2 . The component of the field parallel to the diameter cancels due to a symmetrically placed element, leaving the net field to be perpendicular to the diameter and pointing away from the semicircle. ΞΈ P The net field has a magnitude |πΈπΈ| = 1 4ππππ 0 ππ 2 β«02 ππππ ππππ π π 2 sin ππ = ππ 2ππππ 0 π π