HKPhO ? 20061Hong Kong High School Physics Olympiad 2006 2006 ? Written Examination ?Jointly Organized by Education and Manpower Bureau ? The Hong Kong Physical Society ? The Hong Kong University of Science and Technology ?May 28, 2006 2006 ? 5 ? 28 ?Universityniversit ? ?6 by y power Buwer Bu ?g PhysicPhysi ?HKPhO ? 20062The following symbols and constants will be used throughout the examination paper unless otherwise specified: g gravitational acceleration on Earth surface, 9.8 (m/s2) G gravitation constant, 6.67 x 10-11 (N m2/kg2) e charge of an electron, 1.6 x 10-19 (A s) ?0 electrostatic constant, 8.85 x 10-12 (A s)/(V m) me electron mass = 9.11 x 10-31 kg c speed of light in vacuum, 3.0 x 108 m/s Radius of Earth = 6378 km Sun-Earth distance = 1.5 x 1011m Earth-Moon distance = 3.84 x 108 m Density of water = 1.0 x 103kg/m3 Density of iron = 7.7 x 103kg/m3 Density of mercury = 13.6 x 103kg/m3 Speed of sound in air = 340 m/s ?g ?, 9.8 (m/s2) G ?, 6.67 x 10-11 (N m2/kg2) e ?, 1.6 x 10-19 (A s) ?0 ?, 8.85 x 10-12 (A s)/(V m) me ?, 9.11 x 10-31 kg c ?, 3.0 x 108 m/s ? = 6378 km ?-? = 1.5 x 1011m ?-? = 3.84 x 108 m ? = 1.0 x 103kg/m3 ? = 7.7 x 103kg/m3 ?= 13.6 x 103kg/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) ?m g/m/m3 3 x 10103 3kg/mkg/m3 3 0 m/s m/s wing conditionsing conditionAll objects arAll objects a 2) Neglect aiNeglec 3)3) All speAll spe?HKPhO ? 20063Multiple Choice Questions(2 points each. Select one answer in each question.) ? 2 ?MC1 Given that the moon revolves around Earth at a period of about 27.3 days, use the parameters given in page-2 to find the mass of Earth. ? 2 ? 27.3 ? (a) 2.3 x 1024 kg (b) 4.6 x 1024 kg (c) 6.0 x 1024 kg (d) 7.8 x 1024 kg (e) 9.8 x 1024 kg MC2 As shown, a piston chamber of cross section area A is filled with ideal gas. A sealed piston of mass m is right at the middle height of the cylinder at equilibrium. The friction force between the chamber wall and the piston can be ignored. The mass of the rest of the chamber is M. The atmosphere pressure is P0. Now slowly pull the piston upwards, find the maximum value of M such that the chamber can be lifted off the ground. The temperature remains unchanged. ?A? ?m? ? ?P0? ?M?(a)gmgAPM220? (b) gmgAPM20? (c) gmgAPM?0(d)gAPM20? (e) gAPM0?MC3 Find the electrostatic energy of an equilateral triangle of side a with a point charge q at each vertex, excluding the self-energy of the point charges. ?a?q? ?(a)aq2041 ?(b) aq2043 ?(c) aq2023 ?(d)aq2081 ?(e) aq2041 ?MC4 Two cars A and B are moving towards each other along the same line at 2/3 of the sound speed. Car-A sends out continuous sound waves at frequency f. The frequency of sound heard by the driver of car-B is _. ? A ? B ? 2/3 ?A ?f?B ? ?_? (a) 5f (b) 9f (c) f/5 (d) f/9 (e) f?gAP 2 20Pe) ?g gAP APMM0 0P P P? ?energy of anenergy of an vertex, excludinrtex, exclu ? ?a aq q20 0?(d)(d)?aq q2 208 81 1 ?C4?wards, ds, ed off d off ? ? ? ?mgmg?HKPhO ? 20064MC5 As shown, the tiny ball at the end of the thread of length 100 cm has a mass of 0.6 g and carries charge 5.88 x 10-6 C. It is in a horizontal electric field of intensity 1000 N/C (Newton per Coulomb). Find the vibration frequency of the ball near its equilibrium position. ?0.6 g?5.88 x 10-6 C?100 cm?1000 N/C? ? (a) 0.70 Hz (b) 0.59 Hz (c) 0.50 Hz (d) 3.2 Hz (e) 6.4 Hz MC6 As shown below, a plane microwave is normally incident on four evenly spaced identical narrow slits S1, S2, S3 and S4. XY is a line parallel to the plane of the four slits and far away from the slits. Point-X is at equal distance to slits S2 and S3. When only slits S2 and S3 are open, the wave intensity at point-X reaches the maximum value of A, and that at point-Y is zero. When all four slits are open, the intensity at point-X is _