here-is-a-question-really-troubling-me-A-cylindrical-tube-rolling-down-a-slope-of-inclination-moves-a-distance-L-in-the-time-T-The-equation-relating-these-quantities-is-L-3-a-2-P-QT-2-sin

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Question Number 31149 by NECx last updated on 03/Mar/18

$$hereisaquestionreallytroubling$$$$me.$$$$$$$$Acylindricaltuberollingdowna$$$$slopeofinclination\theta movesa$$$$distanceLinthetimeT.The$$$$equationrelatingthesequantitiesis$$$$$$$$L(3+\frac{a^2}{P})={QT}^2\sin \theta whereais$$$$theinternalradiusofthetubeand$$$$PandQareconstants.Whatare$$$$theunitsofPandQ?$$

Commented by NECx last updated on 03/Mar/18

$$hereiswhatIdid\dots ..$$$$$$$$2gh=v^2(1+K^2/r^2)$$$$$$$$2gLsin\theta =v^2(1+k^2/r^2)$$$$$$$$v^2(1+k^2/r^2)=2gL\sin \theta$$$$$$$$\left(\frac{L^2}{T^2}\right)(1+k^2/r^2)=2gLsin\theta$$$$$$$$L(1+k^2/r^2)=2{gT}^{2}sin\theta \dots ..\left(1\right)$$$$L(3+a^2/P)={QT}^2\sin \theta \dots \dots .\left(2\right)$$$$$$$$\therefore P=L^{2}andQ=g={LT}^{-2}$$$$$$$$Ireallyhaveadoubtonthisplease$$$$checkandcorrect.Thanks$$

Answered by mrW2 last updated on 03/Mar/18

$$Ifyoujustneedtoknowtheunitsof$$$$PandQ,you{don}^{\prime }tneedto$$$$knowalltheformula,evenyou{don}^{\prime }t$$$$needtounderstandphysics.$$$$\frac{a^2}{P}hasthesameunitas3,soPhas$$$$thesameunitas{a}^2,i.e.\left[L^2\right].$$$$Theunitofleftsideis\left[L\right],theright$$$$sidemustalsohavethisunit.$$$$sin\theta hasnounit.$$$$Thastheunit\left[T\right].$$$$\Rightarrow \left[Q\right]\times \left[T^2\right]=\left[L\right]$$$$\Rightarrow \left[Q\right]=\left[\frac{L}{T^2}\right]$$$$i.e.theunitofQis\left[\frac{L}{T^2}\right],e.g.m/s^2.$$

Commented by NECx last updated on 03/Mar/18

$$oh\dots .Thanks$$

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