1CHAPTER ONEPhysics and the Life SciencesMULTIPLE CHOICE QUESTIONSMultiple Choice 1.1Correct Answer (c).mbraindirectly proportionaltoMbodymeans that b = +1 in:bbrainbodyma M(1)Note that the coefficientbis the slope of thecurve after the natural logarithm is taken onboth sides of Eq. [1].Multiple Choice 1.2CorrectAnswer(c).Wecanargueintwoways:physically,wenotethatthesloperepresentsanactualphysicalrelation.Replotting data by using another unit systemcannot change the physical facts. The originalrelationship is given by:bbrainbodyma M(1)Mathematically, plottingmbrainin unit g meansthat we use values that are larger by a factor of1000 on the left side in Eq. [1]. Thus, for Eq.[1] to remain correct, the prefactor must alsobe larger by a factor of 1000. In Eq. [2] wetake the natural logarithm on both sides of Eq.[1], with the brain mass in unitkgon the right–hand side:ln()lnln()brainbodymkgabMkg(2)In Eq. [3] we rewrite Eq. [1] once more withnatural logarithms, but use the brain mass inunitg:ln()ln(1000 )ln()brainbodymgabMkg(3)in which ln (1000a) = ln 1000 + lna.Eqs. [2] and [3] differ only in that a constantterm, ln1000 = 6.908, is added in the secondcase. This represents a vertical shift of thecurve, but not a change in its slope.Multiple Choice 1.3CorrectAnswer(e).Theprecisionofeachnumber is represented by the smaller power ofteninthenumber.Smallerpowersoftenindicate more precise numbers. (d) is the leastprecise number since the smallest power of tenis 1011for the last digit. (a) follows with aprecision of 106, (b) with 10-2, (c) with 10-6,and (e) is the most precise with 10-18being thesmallest power of ten in the number.Multiple Choice 1.4Correct Answer (a). The number of significantfigures in the number represents its accuracy.The more significant figures a number has, themoreaccuratethenumberis.Inorderofincreasingaccuracy,(e)hasonlyonesignificant figure, (d) has two, both (b) and (c)have four, and (a) is the most accurate withfive significant figures.CONCEPTUAL QUESTIONSConceptual Question 1.1No.Webuildphysicalmodelstodescribeobservations of the world around us. Theseobservationsfacelimitationsthatarethenunavoidably transferred to the physical model.Uponimprovingonourobservations,themodelmightstillbevalid,itmightneedcorrections,ormightbewronginafundamental way. Similarly, to build physicalmodelswearerequiredtomakesomeassumptionsasastartingpoint,theseassumptions form the basis for the physicalmodel. However, further observations mightconfirm or deny the initial assumptions andthus validate or invalidate the physical model.Physical models are therefore under constantrevision and continued testing.Conceptual Question 1.2(a)The number 11 is represented by the digit. Note that 10 in base-12 actually representsthe number 12 in base-10. This is because thesequence of digits one-zero in base-12 means 0120+ 1121when expanded in base-10.(b)Repeated integer division of 3498572 by12 will yield the various digits in base-12:3498572 / 12 = 291547 with 8 as residue, sothat 8 is the digit for 120; 291547 / 12 = 24298with 7 as residue, so that 7 is the digit for 121.Preview Mode
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