Menu Close

Two-similar-spheres-of-the-same-material-have-masses-of-12kg-and250kg-respectively-find-the-radius-of-the-smaller-sphere-if-the-radius-of-the-bigger-shere-is-12-5cm-




Question Number 55918 by imamu222 last updated on 06/Mar/19
Two similar spheres of the same material have masses of 12kg and250kg respectively. find the radius of the smaller sphere if the radius of the bigger shere is 12.5cm
$${Two}\:{similar}\:{spheres}\:{of}\:{the}\:{same}\:{material}\:{have}\:{masses}\:{of}\:\mathrm{12}{kg}\:{and}\mathrm{250}{kg}\:{respectively}.\:{find}\:{the}\:{radius}\:{of}\:{the}\:{smaller}\:{sphere}\:{if}\:{the}\:{radius}\:{of}\:{the}\:{bigger}\:{shere}\:{is}\:\mathrm{12}.\mathrm{5}{cm} \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 06/Mar/19
(M_(small) /M_(large) )=(((4/3)πr_(small) ^3 ρ)/((4/3)πr_(large) ^3 ρ))  (M_s /M_l )=(r_s ^3 /r_l ^3 )→r_s ^3 =r_l ^3 ((M_s /M_l ))  r_s =r_l ((M_s /M_l ))^(1/3) →r_s =12.5(((12)/(250)))^(1/3) ≈4.5428cm
$$\frac{{M}_{{small}} }{{M}_{{large}} }=\frac{\frac{\mathrm{4}}{\mathrm{3}}\pi{r}_{{small}} ^{\mathrm{3}} \rho}{\frac{\mathrm{4}}{\mathrm{3}}\pi{r}_{{large}} ^{\mathrm{3}} \rho} \\ $$$$\frac{{M}_{{s}} }{{M}_{{l}} }=\frac{{r}_{{s}} ^{\mathrm{3}} }{{r}_{{l}} ^{\mathrm{3}} }\rightarrow{r}_{{s}} ^{\mathrm{3}} ={r}_{{l}} ^{\mathrm{3}} \left(\frac{{M}_{{s}} }{{M}_{{l}} }\right) \\ $$$${r}_{{s}} ={r}_{{l}} \left(\frac{{M}_{{s}} }{{M}_{{l}} }\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \rightarrow{r}_{{s}} =\mathrm{12}.\mathrm{5}\left(\frac{\mathrm{12}}{\mathrm{250}}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \approx\mathrm{4}.\mathrm{5428}{cm} \\ $$$$ \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *