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](https://www.tinkutara.com/question/Q52273.png)
$${A}\:{cuboid}\:{block}\:{is}\:{floating}\:{in}\:{a} \\ $$$${liquid}\:{with}\:{half}\:{of}\:{its}\:{volume} \\ $$$${immersed}\:{in}\:{the}\:{liquid}.{When}\:{the} \\ $$$${whole}\:{system}\:{accelerates}\:{upwards} \\ $$$${with}\:{an}\:{acceleration}\:{of}\:{g}/\mathrm{3}\:.\:{The} \\ $$$${fraction}\:{of}\:{volume}\:{immersed}\:{in} \\ $$$${the}\:{liquid}\:{will}\:{be} \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left./\mathrm{2}\:{b}\right)\mathrm{3}/\mathrm{8}\:{c}\right)\mathrm{2}/\mathrm{3}\:{d}\right)\mathrm{3}/\mathrm{4} \\ $$$$ \\ $$$${please}\:{help} \\ $$
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](https://www.tinkutara.com/question/Q52279.png)
$$\rho={density}\:{of}\:{block} \\ $$$$\rho_{{w}} ={density}\:{of}\:{liquid} \\ $$$${w}={fraction}\:{of}\:{volume}\:{immersed} \\ $$$${let}'{s}\:{say}\:{the}\:{volume}\:{of}\:{block}\:{is}\:\mathrm{1}. \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:{w}=\mathrm{0}.\mathrm{5} \\ $$$$\rho{g}={w}\rho_{{w}} {g}=\mathrm{0}.\mathrm{5}\rho_{{w}} {g} \\ $$$$\Rightarrow\rho_{{w}} =\mathrm{2}\rho \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:{w}=? \\ $$$${w}\rho_{{w}} {g}−\rho{g}=\rho{a}=\rho\frac{{g}}{\mathrm{3}} \\ $$$$\Rightarrow{w}=\frac{\mathrm{4}\rho}{\mathrm{3}\rho_{{w}} }=\frac{\mathrm{4}\rho}{\mathrm{3}×\mathrm{2}\rho}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$ \\ $$$$\Rightarrow{answer}\:{c} \\ $$
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.](https://www.tinkutara.com/question/Q52281.png)
$${it}'{s}\:{a}\:{language}\:{trap}! \\ $$$${if}\:{it}\:{is}\:{meant}\:{with}\:“{the}\:{whole}\:{system}''\:{the} \\ $$$${block}\:{and}\:{the}\:{liquid}\:{together},\:{then} \\ $$$${the}\:{answer}\:\left({a}\right)\:{is}\:{correct}.\:{but}\:{i},\:{maybe} \\ $$$${the}\:{most}\:{of}\:{other}\:{people}\:{understand} \\ $$$${that}\:{the}\:{tank}\:{is}\:{meant},\:{then}\:{answer} \\ $$$$\left({c}\right)\:{is}\:{correct}.\:{so}\:{this}\:{is}\:{not}\:{a}\:{good} \\ $$$${question}.\:{a}\:{good}\:{question}\:{should}\:\:{let} \\ $$$${the}\:{students}\:{understand}\:{what}\:{is} \\ $$$${exactly}\:{meant}\:{with}\:{the}\:{question}. \\ $$
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.](https://www.tinkutara.com/question/Q52280.png)
$${Thank}\:{you}\:{sir}\:{but}\:{the}\:{answer}\:{in}\:{the} \\ $$$${file}\:{says}\:{answer}\:{is}\:{a}. \\ $$$$ \\ $$$${see}\:{their}\:{explanation} \\ $$$$ \\ $$$${fraction}\:{of}\:{volume}\:{immersed}\:{in} \\ $$$${the}\:{liquid}\:.{It}\:{depends}\:{on}\:{the} \\ $$$${densities}\:{of}\:{the}\:{block}\:{and}\:{liquid}. \\ $$$${So}\:{there}\:{will}\:{be}\:{no}\:{change}\:{in}\:{it}\:{if} \\ $$$${system}\:{moves}\:{upward}\:{or}\:{downwards} \\ $$$${with}\:{constant}\:{velocity}\:{or}\:{some} \\ $$$${acceleration}. \\ $$
Commented by Necxx last updated on 05/Jan/19
![wow.....Thanks a lot.Its clear now](https://www.tinkutara.com/question/Q52283.png)
$${wow}…..{Thanks}\:{a}\:{lot}.{Its}\:{clear}\:{now} \\ $$
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.](https://www.tinkutara.com/question/Q52310.png)
$${we}\:{can}\:{image}\:{the}\:{block}\:{is}\:{floating}\:{in} \\ $$$${water}\:{in}\:{a}\:{tank}\:{which}\:{is}\:{placed}\:{in}\:{a} \\ $$$${lift}.\:{when}\:{the}\:{lift}\:\left({tank}\right)\:\left({this}\:{is}\:{what}\:{we}\right. \\ $$$$\left.{usually}\:{understand}\:{as}\:{the}\:{whole}\:{system}\right) \\ $$$${moves}\:{upwards}\:{with}\:{an}\:{acceleration} \\ $$$${g}/\mathrm{3},\:{we}\:{know}\:{the}\:{block}\:{will}\:{immerse} \\ $$$${more}\:{into}\:{the}\:{water}\:{than}\:{before}.\: \\ $$$${but}\:{the}\:{questioner}\:{means}\:{the}\:{block} \\ $$$${will}\:{also}\:{be}\:{given}\:{the}\:{same}\:{acceleration} \\ $$$${as}\:{the}\:{tank}.\:{this}\:{is}\:{only}\:{the}\:{case}\:{when} \\ $$$${the}\:{block}\:{doesn}'{t}\:{float}\:{freely}\:{in}\:{water}, \\ $$$${but}\:{is}\:{tightly}\:{connected}\:{with}\:{the}\:{tank}. \\ $$$${when}\:{the}\:{block}\:{is}\:{tightly}\:{fixed}\:{with} \\ $$$${the}\:{tank},\:{the}\:{block}\:{can}\:{certainly}\:{not} \\ $$$${immerse}\:{more}\:{or}\:{less}\:{into}\:{the}\:{water}. \\ $$$${so}\:{again},\:{the}\:{question}\:\left({better}\:{to}\:{say}\right. \\ $$$$\left.{the}\:{answer}\:{given}\right)\:{is}\:{not}\:{good},\:{it}'{s} \\ $$$${not}\:{from}\:{this}\:{world}. \\ $$
Commented by peter frank last updated on 06/Jan/19
![perfect](https://www.tinkutara.com/question/Q52320.png)
$${perfect}\: \\ $$