A-cuboid-block-is-floating-in-a-liquid-with-half-of-its-volume-immersed-in-the-liquid-When-the-whole-system-accelerates-upwards-with-an-acceleration-of-g-3-The-fraction-of-volume-immersed-in-the-liq

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Question Number 52273 by Necxx last updated on 05/Jan/19

$$Acuboidblockisfloatingina$$$$liquidwithhalfofitsvolume$$$$immersedintheliquid.Whenthe$$$$wholesystemacceleratesupwards$$$$withanaccelerationofg/3.The$$$$fractionofvolumeimmersedin$$$$theliquidwillbe$$$$a)1/2b)3/8c)2/3d)3/4$$$$$$$$pleasehelp$$

Answered by mr W last updated on 05/Jan/19

$$\rho =densityofblock$$$${\rho }_w=densityofliquid$$$$w=fractionofvolumeimmersed$$$${let}^{\prime }ssaythevolumeofblockis1.$$$$$$$$\left(1\right)w=0.5$$$$\rho g=w{\rho }_{w}g=0.5{\rho }_{w}g$$$$\Rightarrow {\rho }_w=2\rho$$$$$$$$\left(2\right)w=?$$$$w{\rho }_{w}g-\rho g=\rho a=\rho \frac{g}{3}$$$$\Rightarrow w=\frac{4\rho }{3{\rho }_w}=\frac{4\rho }{3\times 2\rho }=\frac{2}{3}$$$$$$$$\Rightarrow answerc$$

Commented by mr W last updated on 05/Jan/19

$${it}^{\prime }salanguagetrap!$$$$ifitismeantwith“thewhole{system}^{″}the$$$$blockandtheliquidtogether,then$$$$theanswer\left(a\right)iscorrect.buti,maybe$$$$themostofotherpeopleunderstand$$$$thatthetankismeant,thenanswer$$$$\left(c\right)iscorrect.sothisisnotagood$$$$question.agoodquestionshouldlet$$$$thestudentsunderstandwhatis$$$$exactlymeantwiththequestion.$$

Commented by Necxx last updated on 05/Jan/19

$$Thankyousirbuttheanswerinthe$$$$filesaysanswerisa.$$$$$$$$seetheirexplanation$$$$$$$$fractionofvolumeimmersedin$$$$theliquid.Itdependsonthe$$$$densitiesoftheblockandliquid.$$$$Sotherewillbenochangeinitif$$$$systemmovesupwardordownwards$$$$withconstantvelocityorsome$$$$acceleration.$$

Commented by Necxx last updated on 05/Jan/19

$$wow\dots ..Thanksalot.Itsclearnow$$

Commented by mr W last updated on 06/Jan/19

$$wecanimagetheblockisfloatingin$$$$waterinatankwhichisplacedina$$$$lift.whenthelift\left(tank\right)(thisiswhatwe$$$$usuallyunderstandasthewholesystem)$$$$movesupwardswithanacceleration$$$$g/3,weknowtheblockwillimmerse$$$$moreintothewaterthanbefore.$$$$butthequestionermeanstheblock$$$$willalsobegiventhesameacceleration$$$$asthetank.thisisonlythecasewhen$$$$theblock{doesn}^{\prime }tfloatfreelyinwater,$$$$butistightlyconnectedwiththetank.$$$$whentheblockistightlyfixedwith$$$$thetank,theblockcancertainlynot$$$$immersemoreorlessintothewater.$$$$soagain,thequestion(bettertosay$$$$theanswergiven)isnotgood,{it}^{\prime }s$$$$notfromthisworld.$$

Commented by peter frank last updated on 06/Jan/19

$$perfect$$

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