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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/3 . The  fraction of volume immersed in  the liquid will be  a)1/2 b)3/8 c)2/3 d)3/4    please help
$${A}\:{cuboid}\:{block}\:{is}\:{floating}\:{in}\:{a} \\ $$$${liquid}\:{with}\:{half}\:{of}\:{its}\:{volume} \\ $$$${immersed}\:{in}\:{the}\:{liquid}.{When}\:{the} \\ $$$${whole}\:{system}\:{accelerates}\:{upwards} \\ $$$${with}\:{an}\:{acceleration}\:{of}\:{g}/\mathrm{3}\:.\:{The} \\ $$$${fraction}\:{of}\:{volume}\:{immersed}\:{in} \\ $$$${the}\:{liquid}\:{will}\:{be} \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left./\mathrm{2}\:{b}\right)\mathrm{3}/\mathrm{8}\:{c}\right)\mathrm{2}/\mathrm{3}\:{d}\right)\mathrm{3}/\mathrm{4} \\ $$$$ \\ $$$${please}\:{help} \\ $$
Answered by mr W last updated on 05/Jan/19
ρ=density of block  ρ_w =density of liquid  w=fraction of volume immersed  let′s say the volume of block is 1.    (1) w=0.5  ρg=wρ_w g=0.5ρ_w g  ⇒ρ_w =2ρ    (2) w=?  wρ_w g−ρg=ρa=ρ(g/3)  ⇒w=((4ρ)/(3ρ_w ))=((4ρ)/(3×2ρ))=(2/3)    ⇒answer c
$$\rho={density}\:{of}\:{block} \\ $$$$\rho_{{w}} ={density}\:{of}\:{liquid} \\ $$$${w}={fraction}\:{of}\:{volume}\:{immersed} \\ $$$${let}'{s}\:{say}\:{the}\:{volume}\:{of}\:{block}\:{is}\:\mathrm{1}. \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:{w}=\mathrm{0}.\mathrm{5} \\ $$$$\rho{g}={w}\rho_{{w}} {g}=\mathrm{0}.\mathrm{5}\rho_{{w}} {g} \\ $$$$\Rightarrow\rho_{{w}} =\mathrm{2}\rho \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:{w}=? \\ $$$${w}\rho_{{w}} {g}−\rho{g}=\rho{a}=\rho\frac{{g}}{\mathrm{3}} \\ $$$$\Rightarrow{w}=\frac{\mathrm{4}\rho}{\mathrm{3}\rho_{{w}} }=\frac{\mathrm{4}\rho}{\mathrm{3}×\mathrm{2}\rho}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$ \\ $$$$\Rightarrow{answer}\:{c} \\ $$
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 (a) is correct. but i, maybe  the most of other people understand  that the tank is meant, then answer  (c) is correct. so this is not a good  question. a good question should  let  the students understand what is  exactly meant with the question.
$${it}'{s}\:{a}\:{language}\:{trap}! \\ $$$${if}\:{it}\:{is}\:{meant}\:{with}\:“{the}\:{whole}\:{system}''\:{the} \\ $$$${block}\:{and}\:{the}\:{liquid}\:{together},\:{then} \\ $$$${the}\:{answer}\:\left({a}\right)\:{is}\:{correct}.\:{but}\:{i},\:{maybe} \\ $$$${the}\:{most}\:{of}\:{other}\:{people}\:{understand} \\ $$$${that}\:{the}\:{tank}\:{is}\:{meant},\:{then}\:{answer} \\ $$$$\left({c}\right)\:{is}\:{correct}.\:{so}\:{this}\:{is}\:{not}\:{a}\:{good} \\ $$$${question}.\:{a}\:{good}\:{question}\:{should}\:\:{let} \\ $$$${the}\:{students}\:{understand}\:{what}\:{is} \\ $$$${exactly}\:{meant}\:{with}\:{the}\:{question}. \\ $$
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.
$${Thank}\:{you}\:{sir}\:{but}\:{the}\:{answer}\:{in}\:{the} \\ $$$${file}\:{says}\:{answer}\:{is}\:{a}. \\ $$$$ \\ $$$${see}\:{their}\:{explanation} \\ $$$$ \\ $$$${fraction}\:{of}\:{volume}\:{immersed}\:{in} \\ $$$${the}\:{liquid}\:.{It}\:{depends}\:{on}\:{the} \\ $$$${densities}\:{of}\:{the}\:{block}\:{and}\:{liquid}. \\ $$$${So}\:{there}\:{will}\:{be}\:{no}\:{change}\:{in}\:{it}\:{if} \\ $$$${system}\:{moves}\:{upward}\:{or}\:{downwards} \\ $$$${with}\:{constant}\:{velocity}\:{or}\:{some} \\ $$$${acceleration}. \\ $$
Commented by Necxx last updated on 05/Jan/19
wow.....Thanks a lot.Its clear now
$${wow}…..{Thanks}\:{a}\:{lot}.{Its}\:{clear}\:{now} \\ $$
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 (tank) (this is what we  usually understand as the whole system)  moves upwards with an acceleration  g/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 (better to say  the answer given) is not good, it′s  not from this world.
$${we}\:{can}\:{image}\:{the}\:{block}\:{is}\:{floating}\:{in} \\ $$$${water}\:{in}\:{a}\:{tank}\:{which}\:{is}\:{placed}\:{in}\:{a} \\ $$$${lift}.\:{when}\:{the}\:{lift}\:\left({tank}\right)\:\left({this}\:{is}\:{what}\:{we}\right. \\ $$$$\left.{usually}\:{understand}\:{as}\:{the}\:{whole}\:{system}\right) \\ $$$${moves}\:{upwards}\:{with}\:{an}\:{acceleration} \\ $$$${g}/\mathrm{3},\:{we}\:{know}\:{the}\:{block}\:{will}\:{immerse} \\ $$$${more}\:{into}\:{the}\:{water}\:{than}\:{before}.\: \\ $$$${but}\:{the}\:{questioner}\:{means}\:{the}\:{block} \\ $$$${will}\:{also}\:{be}\:{given}\:{the}\:{same}\:{acceleration} \\ $$$${as}\:{the}\:{tank}.\:{this}\:{is}\:{only}\:{the}\:{case}\:{when} \\ $$$${the}\:{block}\:{doesn}'{t}\:{float}\:{freely}\:{in}\:{water}, \\ $$$${but}\:{is}\:{tightly}\:{connected}\:{with}\:{the}\:{tank}. \\ $$$${when}\:{the}\:{block}\:{is}\:{tightly}\:{fixed}\:{with} \\ $$$${the}\:{tank},\:{the}\:{block}\:{can}\:{certainly}\:{not} \\ $$$${immerse}\:{more}\:{or}\:{less}\:{into}\:{the}\:{water}. \\ $$$${so}\:{again},\:{the}\:{question}\:\left({better}\:{to}\:{say}\right. \\ $$$$\left.{the}\:{answer}\:{given}\right)\:{is}\:{not}\:{good},\:{it}'{s} \\ $$$${not}\:{from}\:{this}\:{world}. \\ $$
Commented by peter frank last updated on 06/Jan/19
perfect
$${perfect}\: \\ $$

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