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