HKPhO 2008 Hong Kong Physics Olympiad 2008 2008 Written Examination Jointly Organized by Education Bureau The Hong Kong Physical Society The Hong Kong University of Science and Technology May 25, 2008 2008 5 25 1 HKPhO 2008 Rules and Regulations 1.All questions are in bilingual versions. You can answer in either Chinese or English. 2.The multiple-choice answer sheet will be collected 1.5 hours after the start of the contest. You can start answering the open-ended questions any time after you have completed the multiple-choice questions without waiting for further announcement. 3.Please follow the instructions on the multiple-choice answer sheet, and use a HB pencil to writeyour8-dightParticipantIDnumberinthefieldofI.D.No.,andfilloutthe appropriate circles fully. After that, write your English name in the space provided and your Hong Kong ID number in the field of Course number & Section No. HBI.D. No. 8Course & Section No. 4.On the cover of the answer book, please write your Hong Kong ID number in the field of Course Title, and write your English name in the field of Student Name and your 8-dightParticipantIDnumberinthefieldofStudentNumber.Youcanwriteyour answers on both sides of the sheets in the answer book. Course Title Student Name Student Number 8 5.After you have made the choice in answering a multiple choice question, fill the corresponding circle on the multiple-choice answer sheet fully using a HB pencil. HB 6.The information provided in the text and in the figure of a question should be put to use together. 7.Some open problems are quite long. Read the entire problem before attempting to solve them. If you cannot solve the whole problem, try to solve some parts of it. You can even use the answers in some unsolved parts as inputs to solve the others parts of a problem. 2 HKPhO 2008 The following symbols and constants are used throughout the examination paper unless otherwise specified: g gravitational acceleration on Earth surface, 9.8 (m/s2) G gravitational constant, 6.67 10-11 (N m2/kg2) e charge of an electron, 1.6 10-19 (A s) 0 electrostatic constant, 8.85 10-12 (A s)/(V m) me electron mass =9.11 10-31 kg c speed of light in vacuum, 3.0 108 m/s Radius of Earth =6378 km Sun-Earth distance (=1 Astronomical Unit (AU)) =1.5 1011 m Earth-Moon distance =3.84 108 m Mass of the sun =1.99 1030 kg Density of water =1.0 103 kg/m3Density of iron =7.7 103 kg/m3Density of mercury =13.6 103 kg/m3Speed of sound in air =340 m/s g , 9.8 (m/s2) G , 6.67 10-11 (N m2/kg2) e , 1.6 10-19 (A s) 0 , 8.85 10-12 (A s)/(V m) me , 9.11 10-31 kg c , 3.0 108 m/s =6378 km - (=1 ) =1.5 1011 m - =3.84 108 m =1.99 1030 kg =1.0 103 kg/m3 =7.7 103 kg/m3=13.6 103 kg/m3=340 m/s The following conditions will be applied unless otherwise specified: 1)All objects are near Earth surface and the gravity is pointing downwards. 2)Neglect air resistance. 3)All speeds are much smaller than the speed of light. 1) 2) 3) 3 HKPhO 2008 Multiple Choice Questions(2 points each. Select one answer in each question.) 2 The MC questions with the * sign may require information on page-3. * MC1 An object in constant acceleration motion with zero initial velocity covers 1 meter within the 1st second. How many meters will it cover within the 4th second? 1 (a) 7 (b) 1(c) 9(d) 3(e) 16 MC2 0 0x y +r r0 0Spaceship A moves at velocity 40( ) km/s, while spaceship B moves at 30 ( x y r r0 0) km/s. Find the relative velocity in the unit of km/s between the two ships. x y +r r0 0-A 40( )-B30 ( x y r r0 010) x y +r r0 070 x y +r r0 010 (a)10 (b)10 (c)70x y +r r0 010 (d)10x z +r r0 010 x y r r(e)10 MC3* J upiter revolves around the sun at 11 years and 315 days per revolution. Find the distance between J upiter and Sun in terms of astronomical unit (A. U.). 11315 (a) 5.2 (b) 1.0 (c) 11.9(d) 15(e) 3.0 MC4 An object is in motion with constant acceleration. Which of the following statement is correct? (a) The object must move in a straight line. (b) The distance traveled must be proportional to the square of the time. (c) The speed of the object must increase uniformly with time. (d) The velocity must be constant. (e) The total external force must do work to the object. (a) (b) (c) (d) (e) 4 HKPhO 2008 MC5 An object is placed on the left side of a positive lens and the real image is formed on the right side of the lens. If the object is moved slightly to the right, the image will _______. (a) not move (b) move to the left(c) move to the right (d) move up (e) move down _______ (a) (b) (c) (d) (e) MC6 Same initial condition as MC5 above. If the upper half of the lens is covered with black cloth, the image will _____ . (a) totally disappear (b) move up (c) move down (d) become brighter(e) become dimmer MC5_______ (a) (b) (c) (d) (e) MC7Five circuits are shown below.The batteries all have the same voltage V and all resistors have the same resistance R. In which circuit does the battery output the most power? VR

VRRRRAVRRRRAVRRRBVRRRBVRRRDVRRRDVR RCVR RCVREVRE (a) A(b) B(c) C (d) D(e) E 5 HKPhO 2008 MC8 A 20 F capacitor charged to 2.0 kV and a 40 F capacitor charged to 4.0 kV are connected to each other, with the positive plate connected to the positive plate, and the negative plate to the negative plate. What is the final charge on the 20 F capacitor? 20 F 2.0 kV 40 F 4.0 kV 20 F ? (a)50 mC(b)200 mC(c) 40 mC (d) 67 mC(e) 120 mC MC9 A cylinder is filled with ideal gas with pressure P. The gas is then heated up by an external source and has doubled its volume and temperature, while half the gas has leaked out. Find the pressure of the remaining gas. P (a)2P(b)4P (c) P (d) 0.5P(e) 0.25P MC10 In the circuit, the electric current through the battery is _____ Amperes. 4V 4V44244V 4V44244V 4V4424_____ (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 MC11 Which of the process below DOES NOT involve energy transfer? (a) Lifting a cup(b) Turning on a lamp (c) Burning some wood d) Motion of a simple pendulum (e) Moon revolving around Earth in circular motion (a) (b) (c) d) (e) MC12* Ignore friction between water and pipe wall. Water is pumped from a reservoir up to a height of 10 m at the rate of 30 kg per second through a pipe of 2.0 10-3 m2 in cross section area. Find the pumping power. 2.0 10-33010 (a) 6315 (b) 2940 (c) 3573 (d) 1305 (e) 4960 6 HKPhO 2008 MC13 As shown, a triangular coil is moving into a uniform magnetic field region (field pointing into the paper) at uniform velocity. Which of the following statements is/are correct? (1)An induced current flows from P to Q through resistor R.(2)The magnetic flux passing through the coil is increasing at a uniform rate. (3) The induced emf is increasing at a uniform rate (1) R P Q (2) (3) (a) (1)(b) (3)(c) (1) and (2) (d)(2) and (3)(e) (1) and (3) MC14 Two uniform circular discs of the same material and thickness are adhered together at point-N. Both discs lie in the same vertical plane. The rigid body is hinged at point-P and it can rotate freely about P in the vertical plane. PO OM and ON =2 NM, where point-O and point-M are the centres of the discs. When static equilibrium is reached, find the angle between PO and the vertical direction. NPPO M PO OM ON =2 NMPO (a)16.7o(b) 26.6o (c)30o(d)36.9o(e)11.7o MC15 Two monkeys of the same weight are holding tightly the two ends of a rope with negligible mass. The rope passes through a smooth pulley, as shown in the figure. The two monkeys are initially at rest. Now the left monkey starts to climbs up the rope at an average speed v relative to the pulley. Find its average speed relative to the right monkey. v P QRmotionP QRmotionOPMN OPMN (a)0(b) v upwards (c) 2v upwards (d) v downwards (e)2v downwards7 HKPhO 2008 MC16 V2CCCV2CCCAs shown, find the charge on one of the capacitors with capacitance C. C 12CV (d)1CV (a)2CV(b) CV(c)418CV (e) MC17 Same initial condition as MC16. If the battery is suddenly taken away and the switch shown in the circuit diagram is closed, find the total charge that will pass through the switch. MC16 (a)2CV(b) CV(c)12CV (d)1CV4(e)18CV MC18* An object of volume V is submerged in a liquid of density . It has a flat bottom of area A which is at a depth of H in the liquid, and a dome shaped top. Find the total force of liquid acting on the top of the object. (a)| | HAg Vg HAg Vg and upward(b) | | and downward V2CCCV2CCCV2CCC Vg Vg (c)and downward(d)and upwardHAg (e)and upward V HA | HAg Vg HAg Vg(c) Vg (a)|(b) | | Vg (e)HAg (d) MC19 An AC generator consists of 6 turns of rectangular wire coil. Each turn has an area of 0.040 m2. The coil rotates in a uniform field (B =0.20 T) at a constant frequency of 50 Hz. Find the maximum induced electro-motive force. 6 0.040 0.20 T 50 (a)4.8 V(b) 2.5 V(c) 3.0 V(d) 15 V (e) 7.5 V 8 HKPhO 2008 MC20 A cup of water is placed in a car under constant acceleration to the left, as shown. Inside the water is a small air bubble. The following figures show five situations of the shape of the water surface and the direction of motion of the bubble as indicated by the arrow on the bubble. Which one is correct? arAB C D E (a) A(b) B(c) C (d) D(e) E End of MCs Open Problems Total 5 problems 5 The Open Problem(s) with the * sign may require information on page-3. * Q1* (10 points) A particle of mass m carrying charge q is placed mid-way between two fixed point charges, each carrying charge Q. All three particles are on the x-axis. The distance between the fixed charges is 2d. The particle is confined to move along the x-axis only.(a)Determine whether the equilibrium position of the particle is stable when q and Q are of the same sign or of opposite sign. (3 points) (b)In the case of stable equilibrium, find the vibration frequency of small amplitude oscillation of the particle. (7 points)(Hint: for x