t 3 t 4 Part A: Multiple Choice Canadian Association of Physicists 1999 Prize Exam

Transcription

1 Cndin Assocition of Physicists 1999 Prize Exm This is three hour exm. Ntionl rnking nd prizes will be bsed on student s performnce on both sections A nd B of the exm. However, performnce on the multiple choice questions in prt A will be used to determine whose written work in prt B will be mrked for prize considertion by the Ntionl Committee. The questions in prt B of the exm hve rnge of difficulty. Plese be creful to gther s mny of the esier mrks s possible before venturing into more difficult territory. In some cses n nswer to prt () of question is needed for prt (b). Should you not be ble to solve prt (), ssume likely solution nd ttempt the rest of the question nywy. No student is expected to completely finish this exm nd prts of ech question re very chllenging. Non-progrmmble clcultors my be used. Plese be very creful to nswer the multiple choice questions on the nswer crd/sheet provided to you nd, most importntly, write your solutions to the three written problems on seprte sheets s they will be mrked by different people in different prts of Cnd. Good luck. Dt Speed of light c = m/s Grvittionl constnt G = Nm 2 /kg 2 Rdius of Erth R E = m Rdius of Moon R M = m Mss of Erth M E = kg Mss of Moon M M = kg Mss of Sun M S = kg Rdius of Moon s orbit R EM = m Rdius of Erth s orbit R ES = m Accelertion due to grvity g =9.81 m/s 2 Fundmentl chrge e = C Mss of electron m e = kg Mss of proton m p = kg Mss of neutron m n = kg Plnck s constnt h = Js Coulomb s constnt 1/4πɛ o = Nm 2 /C 2 Permebility of free spce µ o =4π 10 7 N/A 2 Speed of sound in ir v s = 340 m/s Density of ir ρ =1.2 kg/m 3 Boltzmnn constnt k = J/K Absolute zero T =0K,T = 273 C Energy Conversion 1 cl=4.184 J Avogdro s number N A = mol 1 Prt A: Multiple Choice Question 1 The time dependence of the ccelertion of cr is s shown. Which time corresponds to the mximum speed of the cr? () t 1 (b) t 2 (c) t 3 (d) t 4 t 3 t 4 t 1 t 2 Question 2 Two identicl loudspekers re supplied with identicl sinusoidl signls. They re plced close to one nother in room nd it is noted tht there re regions of incresed nd decresed sound intensity in the vicinity of the spekers. Which of the following ctions will not chnge this pttern? () Moving one of the spekers. (b) Chnging the mplitude of the signl. (c) Chnging the frequency of the signl. (d) Replcing the ir in the room with Helium gs. Question 3 Two blck objects of the sme dimeter, sphere nd disc, re plced in front of uniform bem of light. The plne of the disc is perpendiculr to the light rys. The force cting upon them by the light is: () zero (b) bigger on the disc. (c) bigger on the sphere. (d) the sme on both. Question 4 A 1 kg mss rests on the ground, t se-level nd t the equtor. Wht would its weight be if the erth were spinning ten times fster thn is presently the cse? () 9.80 N (b) 3.37 N (c) 6.43 N (d) 9.76 N t

2 Question 5 An idel Ammeter device to mesure current in n electricl circuit should hve n internl resistnce which is, () zero. (b) infinite. (c) equl to the resistnce of the circuit s lod. (d) equl to the internl resistnce of the circuit s power source. Question 6 A 100,000 kg ircrft drops 1000 kg pckge of supplies over n rctic reserch sttion. Wht pproximte force is felt by the 100 kg pilot t the instnt of the relese? () 1 N (b) 10 N (c) 100 N (d) zero Question 7 A converging lens forms n imge of n object on screen. The imge is rel nd hs twice the size of the object. If the positions of the screen nd the object re interchnged, leving the lens in its originl position, wht is the new imge size on the screen? () Twice the object size. (b) Sme s the object size. (c) Hlf the object size. (d) Cn t sy s it depends on the focl length of the lens. Question 8 A bucket full of wter is ttched to the end of rope nd llowed to swing bck nd forth s pendulum from fixed support. The bucket hs hole in its bottom tht llows wter to lek out. How does the period of motion chnge with the loss of wter? () The period does not chnge. (b) The period continuously decreses. (c) The period continuously increses. (d) The period increses to some mximum nd then decreses gin. Question 9 A pencil is plced verticlly on tble top with its pointy end up nd its sticky erser end down. As it flls over from this unstble position, its point of contct with the tble remins sttionry. During its fll, the ccelertion of its tip, () remins less thn g t ll times. (b) exceeds g t some point. (c) becomes g just before hitting the tble. (d) is constnt. Question 10 Two 20 g worms climb over 10 cm high, very thin, wll. One worm is thin nd 20 cm long. The other is ft (but still thin compred to its length) nd only 10 cm long. Wht is the rtio of the potentil energy of the thin worm s compred to tht of the ft worm when ech is hlf wy over the top of the wll? () 1:1 (b) 2:1 (c) 2:3 (d) 1:2 Question 11 Suppose tht the Mn Who Skied Down Everest went stright down n incline of 40 to the horizontl nd subject to coefficient of kinetic friction of Strting from rest, how long did it tke him to rech speed of 50 km/hr (Ignore ir resistnce)? () 2.5 s (b) 9.0 s (c) s (d) 2.0 s Question 12 A stone is thrown verticlly downwrd from the edge of cliff with n initil speed of 10 m/s. Just before hitting the ground, it hs finl speed of 30 m/s. If insted, the stone were thrown horizontlly outwrds from the top of the cliff with the sme initil speed s before, wht finl speed would it hve immeditely before hitting the ground? () 10 m/s (b) 20 m/s (c) 30 m/s (d) 40 m/s Question 13 Two objects of equl mss, nd heding towrds ech other with equl speeds, undergo hed-on collision.which of the following sttements is correct? () Their finl velocities must be zero. (b) Their finl velocities my be zero. (c) Ech must hve finl velocity equl to the other s initil velocity. (d) Their velocities must be reduced in mgnitude. 2

3 Question 14 A positive point chrge +Q is plced t x =0nd negtive point chrge Q is plced t x =. The mgnitude of the electrosttic force between the two is F. If nother point chrge +Q is pced t x =, the net force on the chrge t the origin (x =0)is, () 2F in the negtive x-direction. (b) F in the positive x-direction. (c) 5F/4 in the positive x-direction. (d) 2F in the positive x-direction. Question 15 A simple circuit contins n idel bttery nd resistnce R. If second resistor is plced in prllel with the first, () the potentil cross R will decrese. (b) the current through R will decrese. (c) the current delivered by the bttery will increse. (d) the power dissipted by R will increse. Question 16 A positively chrged insultor is brought ner (but does not touch) two metllic spheres tht re in contct. The metllic spheres re then seprted. The sphere which ws initilly frthest from the insultor will hve, () no net chrge. (b) negtive chrge. (c) positive chrge. (d) either positive or negtive chrge. Question 17 A uniform electric field is s shown. How mny of the lbelled points hve the sme electric potentil s the shded point? () 2 (b) 3 (c) 4 (d) 8 E Question 18 A sphericl cpcitor is formed by two metllic nd concentric sphericl shells. The cpcitor is then chrged so tht the outer shell crries positive chrge nd the inner shell crries n equl but negtive chrge. Even if the cpcitor is not connected to ny circuit, the chrge will eventully lek wy due to the smll conductivity of the mteril between the shells. Wht is the chrcter of the mgnetic field induced by this lekge current? () Rdilly outwrds from the inner shell to the outer shell. (b) Rdilly inwrds from the outer shell to the inner shell. (c) Circulr field lines between the shells nd perpendiculr to the rdil direction. (d) No mgnetic field is induced. Question 19 Which of the following hs units of mgnetic field? () kg C 1 (b) kg A 1 (c) N C 1 (d) J A 1 s 1 s 1 m 1 m 1 Question 20 Ner the geogrphic north pole is the mgnetic north pole which is, in fct, south mgnetic pole. At this point, the erth s mgnetic field points stright down. An electron is projected southwrds nd horizontlly from the mgnetic north pole. The mgnetic force on the electron will cuse it to be deflected to the, () Up (b) Down (c) Est (d) West Question 21 A diffrction grting hs 300 lines per mm etched upon it. When light of wvelength 550 nm is normlly incident upon the grting, how mny bright spots pper on screen short distnce wy? () 1 (b) 6 (c) 12 (d) 13 Question 22 Adropofoil(n=1.4) is on glss (n =1.5) sheet nd is observed from directly bove by reflected white light. 3

4 A number of circulr constructive interference bnds re observed for ech colour in the visible spectrum. Approximtely how thick is the oil film where one observes the third blue bnd from the outside edge of the drop. The wvelength of blue light my be tken to be λ b = 450 nm. ir observer Question 25 In the film Armgeddon, stronuts lnd on n steroid nd re ble to wlk round normlly due to the grvittion of the lrge rock. Suppose tht sphericl steroid hs mss M nd rdius R. A sphericl hole of rdius R/2 is excvted from the steriod s shown. Wht is the grvittionl ccelertion t point on the surfce of the steroid t point just bove the excvtion? () 482 nm (b) 675 nm (c) 1125 nm (d) 1350 nm oil R Question 23 A uniform, horizontl bem of light is incident upon prism s shown. The prism is in the shpe of qurtercylinder, of rdius R = 5 cm, nd hs the index of refrction n =1.5. A ptch on the tble top for distnce x from the cylinder is unilluminted. The vlue of x is, () GM R 2 (b) GM 2R 2 (c) GM 8R 2 (d) 7GM 8R 2 R x () 1.71 cm (b) 2.24 cm (c) 2.50 cm (d) 5.00 cm Question 24 Consider the following types of electromgnetic rdition: rdio wves, infr-red, visible light. Which of the following sttements re true? (i) only rdio wves cn be used to trnsmit udio informtion. (ii) only infr-red rdition is emitted by very hot objects. (iii) only visible light cn be detected by humns. () only i is true. (b) only ii is true. (c) only iii is true. (d) None of the sttements re true. 4

5 Prt B Question 1 Four chrges, ech of chrge +e, re t the four corners of squre of side = 1 cm. The four chrges re fixed in plce nd re considered to be of point-size. Grvity plys no role in this question. e + p + p + () Sketch digrm of the electric field due to this chrge system. (b) Wht is the net force cting upon one of the chrges? (c) Wht is the electrosttic potentil energy of this chrge system? (d) Now suppose tht two of the chrges re protons nd the other two re positrons. A positron is the electron s nti-prticle. It hs the sme mss s n electron but chrge of +e. The four chrges re suddenly relesed. Wht re their speeds when they re significnt distnce prt from one nother? e + (c) Remember tht the constnt force is lwys cting upon the first bed. Wht is the time intervl between subsequent collisions between the first nd second beds? Wht then is the verge speed of the first bed? Wht is the speed of the shock wve tht trvels down the wire? (d) If the whole process is repeted, but with collisions which re perfectly inelstic, wht is the terminl speed of the shock wve formed? Question 3 From everydy experience nd observtions, estimte the brightness of full moon s compred to the noon dy sun. Brightness is defined s the luminous intensity s mesured in units of power per unit re. To rrive t resonble numericl estimte, you will need to estimte some physicl prmeters. It is essentil tht you explin the resoning behind your estimtes nd include detiled drwings nd explntions to support your rguments. Question 2 Suppose tht we hve string of eqully spced beds of mss m, their surfces being seprted by distnce d, tht re free to slide without friction on thin wire. Suppose tht constnt force F cts on the first bed, initilly t rest, cusing it to ccelerte long the wire s shown. This force cts only on the first bed nd might be creted by well directed, stedy strem of ir. The first bed will collide with the second, which will in turn collide with the third, nd so on. Suppose tht ll collisions re elstic. F 1 d () Wht is the speed of the first bed immeditely before nd immeditely fter its collision with the second bed? (b) Wht is the speed of the second bed immeditely before nd immeditely fter its collision with the third bed? 5