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Question Number 52273 by Necxx last updated on 05/Jan/19
$${A}\:{cuboid}\:{block}\:{is}\:{floating}\:{in}\:{a} \\ $$$${liquid}\:{with}\:{half}\:{of}\:{its}\:{volume} \\ $$$${immersed}\:{in}\:{the}\:{liquid}.{When}\:{the} \\ $$$${whole}\:{system}\:{accelerates}\:{upwards} \\ $$$${with}\:{an}\:{acceleration}\:{of}\:{g}/\mathrm{3}\:.\:{The} \\ $$$${fraction}\:{of}\:{volume}\:{immersed}\:{in} \\ $$$${the}\:{liquid}\:{will}\:{be} \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left./\mathrm{2}\:{b}\right)\mathrm{3}/\mathrm{8}\:{c}\right)\mathrm{2}/\mathrm{3}\:{d}\right)\mathrm{3}/\mathrm{4} \\ $$$$ \\ $$$${please}\:{help} \\ $$
Answered by mr W last updated on 05/Jan/19
$$\rho={density}\:{of}\:{block} \\ $$$$\rho_{{w}} ={density}\:{of}\:{liquid} \\ $$$${w}={fraction}\:{of}\:{volume}\:{immersed} \\ $$$${let}'{s}\:{say}\:{the}\:{volume}\:{of}\:{block}\:{is}\:\mathrm{1}. \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:{w}=\mathrm{0}.\mathrm{5} \\ $$$$\rho{g}={w}\rho_{{w}} {g}=\mathrm{0}.\mathrm{5}\rho_{{w}} {g} \\ $$$$\Rightarrow\rho_{{w}} =\mathrm{2}\rho \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:{w}=? \\ $$$${w}\rho_{{w}} {g}−\rho{g}=\rho{a}=\rho\frac{{g}}{\mathrm{3}} \\ $$$$\Rightarrow{w}=\frac{\mathrm{4}\rho}{\mathrm{3}\rho_{{w}} }=\frac{\mathrm{4}\rho}{\mathrm{3}×\mathrm{2}\rho}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$ \\ $$$$\Rightarrow{answer}\:{c} \\ $$
Commented by mr W last updated on 05/Jan/19
$${it}'{s}\:{a}\:{language}\:{trap}! \\ $$$${if}\:{it}\:{is}\:{meant}\:{with}\:``{the}\:{whole}\:{system}''\:{the} \\ $$$${block}\:{and}\:{the}\:{liquid}\:{together},\:{then} \\ $$$${the}\:{answer}\:\left({a}\right)\:{is}\:{correct}.\:{but}\:{i},\:{maybe} \\ $$$${the}\:{most}\:{of}\:{other}\:{people}\:{understand} \\ $$$${that}\:{the}\:{tank}\:{is}\:{meant},\:{then}\:{answer} \\ $$$$\left({c}\right)\:{is}\:{correct}.\:{so}\:{this}\:{is}\:{not}\:{a}\:{good} \\ $$$${question}.\:{a}\:{good}\:{question}\:{should}\:\:{let} \\ $$$${the}\:{students}\:{understand}\:{what}\:{is} \\ $$$${exactly}\:{meant}\:{with}\:{the}\:{question}. \\ $$
Commented by Necxx last updated on 05/Jan/19
$${Thank}\:{you}\:{sir}\:{but}\:{the}\:{answer}\:{in}\:{the} \\ $$$${file}\:{says}\:{answer}\:{is}\:{a}. \\ $$$$ \\ $$$${see}\:{their}\:{explanation} \\ $$$$ \\ $$$${fraction}\:{of}\:{volume}\:{immersed}\:{in} \\ $$$${the}\:{liquid}\:.{It}\:{depends}\:{on}\:{the} \\ $$$${densities}\:{of}\:{the}\:{block}\:{and}\:{liquid}. \\ $$$${So}\:{there}\:{will}\:{be}\:{no}\:{change}\:{in}\:{it}\:{if} \\ $$$${system}\:{moves}\:{upward}\:{or}\:{downwards} \\ $$$${with}\:{constant}\:{velocity}\:{or}\:{some} \\ $$$${acceleration}. \\ $$
Commented by Necxx last updated on 05/Jan/19
$${wow}.....{Thanks}\:{a}\:{lot}.{Its}\:{clear}\:{now} \\ $$
Commented by mr W last updated on 06/Jan/19
$${we}\:{can}\:{image}\:{the}\:{block}\:{is}\:{floating}\:{in} \\ $$$${water}\:{in}\:{a}\:{tank}\:{which}\:{is}\:{placed}\:{in}\:{a} \\ $$$${lift}.\:{when}\:{the}\:{lift}\:\left({tank}\right)\:\left({this}\:{is}\:{what}\:{we}\right. \\ $$$$\left.{usually}\:{understand}\:{as}\:{the}\:{whole}\:{system}\right) \\ $$$${moves}\:{upwards}\:{with}\:{an}\:{acceleration} \\ $$$${g}/\mathrm{3},\:{we}\:{know}\:{the}\:{block}\:{will}\:{immerse} \\ $$$${more}\:{into}\:{the}\:{water}\:{than}\:{before}.\: \\ $$$${but}\:{the}\:{questioner}\:{means}\:{the}\:{block} \\ $$$${will}\:{also}\:{be}\:{given}\:{the}\:{same}\:{acceleration} \\ $$$${as}\:{the}\:{tank}.\:{this}\:{is}\:{only}\:{the}\:{case}\:{when} \\ $$$${the}\:{block}\:{doesn}'{t}\:{float}\:{freely}\:{in}\:{water}, \\ $$$${but}\:{is}\:{tightly}\:{connected}\:{with}\:{the}\:{tank}. \\ $$$${when}\:{the}\:{block}\:{is}\:{tightly}\:{fixed}\:{with} \\ $$$${the}\:{tank},\:{the}\:{block}\:{can}\:{certainly}\:{not} \\ $$$${immerse}\:{more}\:{or}\:{less}\:{into}\:{the}\:{water}. \\ $$$${so}\:{again},\:{the}\:{question}\:\left({better}\:{to}\:{say}\right. \\ $$$$\left.{the}\:{answer}\:{given}\right)\:{is}\:{not}\:{good},\:{it}'{s} \\ $$$${not}\:{from}\:{this}\:{world}. \\ $$
Commented by peter frank last updated on 06/Jan/19
$${perfect}\: \\ $$