Question Number 66621 by lalitchand last updated on 17/Aug/19
Commented by lalitchand last updated on 17/Aug/19
$$\mathrm{8}\:\mathrm{iii} \\ $$
Commented by mr W last updated on 18/Aug/19
$${answer}\:{given}\:{in}\:{book}\:{for}\:{Q}\:\mathrm{8}\left({ii}\right)\:{is}\:{wrong}. \\ $$$$ \\ $$$${Q}\:\mathrm{8}\left({iii}\right)\:{in}\:{book}\:{is}\:{not}\:{clear}.\:{if}\:{weight} \\ $$$${of}\:\mathrm{1}\:{kg}\:\left({stone}\right)\:{is}\:\mathrm{10}\:{N}\:{in}\:{water},\:{then} \\ $$$${the}\:{density}\:{of}\:{water}\:{must}\:{be}\:{zero}, \\ $$$${no}\:{matter}\:{what}\:{density}\:{the}\:{stone}\:{has}. \\ $$$${the}\:{answer}\:{in}\:{book}\:{is}\:\mathrm{10}{g}/{cc},\:{but}\:{no} \\ $$$${stone}\:{in}\:{this}\:{world}\:{can}\:{have}\:{such}\:{a} \\ $$$${large}\:{density}. \\ $$$$ \\ $$$$\Rightarrow{book}\:{is}\:{bad} \\ $$
Commented by mr W last updated on 18/Aug/19
$${question}\:{is}\:{wrong},\:{answer}\:{is}\:{wrong}. \\ $$$${answer}\:{to}\:{question}\:\mathrm{8}\left({ii}\right)\:{is}\:{also}\:{wrong}. \\ $$
Commented by lalitchand last updated on 18/Aug/19
$$\mathrm{some}\:\mathrm{one}\:\mathrm{says}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{4g}/\mathrm{cm}^{\mathrm{3}} \\ $$
Commented by lalitchand last updated on 18/Aug/19
$$\mathrm{That}\:\mathrm{means}\:\mathrm{question}\:\mathrm{is}\:\mathrm{wrong} \\ $$
Commented by mr W last updated on 18/Aug/19
$${a}\:{correct}\:{question}\:\mathrm{8}\left({iii}\right)\:{could}\:{be}: \\ $$$$\boldsymbol{{if}}\:\boldsymbol{{the}}\:\boldsymbol{{weight}}\:\boldsymbol{{of}}\:\mathrm{2}\:\boldsymbol{{kg}}\:\boldsymbol{{stone}}\:\boldsymbol{{is}}\:\mathrm{10}\:\boldsymbol{{N}}\:\boldsymbol{{in}} \\ $$$$\boldsymbol{{water}},\:\boldsymbol{{what}}\:\boldsymbol{{is}}\:\boldsymbol{{the}}\:\boldsymbol{{density}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{stone}}? \\ $$$$ \\ $$$${the}\:{answer}\:{were}\:\mathrm{2}\:{g}/{cm}^{\mathrm{3}} . \\ $$$$ \\ $$$${solution}: \\ $$$${let}\:{V}={volume}\:{of}\:{stone},\:{density}\:{is}\:\rho, \\ $$$${mass}\:{is}\:{m}. \\ $$$${V}=\frac{{m}}{\rho} \\ $$$${uptrust}\:{given}\:{by}\:{water}\:{is}\:\rho_{{W}} {gV} \\ $$$${weight}\:{of}\:{stone}\:{in}\:{water}\:{is}\:{then} \\ $$$${G}_{{W}} ={mg}−\rho_{{W}} {gV}={mg}\left(\mathrm{1}−\frac{\rho_{{W}} }{\rho}\right) \\ $$$${with}\:{m}=\mathrm{2}\:{kg},\:{G}_{{W}} =\mathrm{10}\:{N},\:\rho_{{W}} =\mathrm{1}\:{g}/{cm}^{\mathrm{3}} \\ $$$$\mathrm{2}×\mathrm{10}\left(\mathrm{1}−\frac{\mathrm{1}}{\rho}\right)=\mathrm{10} \\ $$$$\Rightarrow\mathrm{1}−\frac{\mathrm{1}}{\rho}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow\rho=\mathrm{2}\:{g}/{cm}^{\mathrm{3}} \\ $$
Commented by mr W last updated on 18/Aug/19
$${you}\:{can}\:{also}\:{see}\:{that}\:{it}\:{is}\:{impossible} \\ $$$${that}\:\mathrm{1}\:{kg}\:{stone}\:{has}\:{a}\:{weight}\:{of}\:\mathrm{10}\:{N} \\ $$$${in}\:{water},\:{because}\:{that}\:{would}\:{request} \\ $$$$\mathrm{1}×\mathrm{10}\left(\mathrm{1}−\frac{\mathrm{1}}{\rho}\right)=\mathrm{10} \\ $$$${but}\:{this}\:{is}\:{not}\:{possible}.\:{therefore} \\ $$$${the}\:{question}\:{in}\:{the}\:{book}\:{is}\:{wrong}. \\ $$