Question Number 132765 by Ahmed1hamouda last updated on 16/Feb/21
Answered by mr W last updated on 16/Feb/21
Commented by mr W last updated on 16/Feb/21
$${G}\left(\frac{\mathrm{7}{a}}{\mathrm{4}},\frac{\mathrm{5}{a}}{\mathrm{4}}\right) \\ $$
Answered by TheSupreme last updated on 16/Feb/21
$${OG}_{\mathrm{1}} =\left({a},\mathrm{2}{a}\right) \\ $$$${OG}_{\mathrm{2}} =\left(\mathrm{2}{a},{a}\right) \\ $$$${A}_{\mathrm{1}} ={A}_{\mathrm{2}} \\ $$$${OG}=\frac{\rho_{\mathrm{1}} {A}_{\mathrm{1}} \left({a}\overset{\rightarrow} {{i}}+\mathrm{2}{a}\overset{\rightarrow} {{j}}\right)+\rho_{\mathrm{2}} {A}_{\mathrm{2}} \left(\mathrm{2}{a}_{\mathrm{1}} \overset{\rightarrow} {{i}}+{a}_{\mathrm{2}} \overset{\rightarrow} {{j}}\right)}{\rho_{\mathrm{1}} {A}_{\mathrm{1}} +\rho_{\mathrm{2}} {A}_{\mathrm{2}} } \\ $$$${OG}={a}\left(\frac{\rho_{\mathrm{1}} +\mathrm{2}\rho_{\mathrm{2}} }{\rho_{\mathrm{1}} +\rho_{\mathrm{2}} }\right)\overset{\rightarrow} {{i}}+{a}\left(\frac{\mathrm{2}\rho_{\mathrm{1}} +\rho_{\mathrm{2}} }{\rho_{\mathrm{1}} +\rho_{\mathrm{2}} }\right)\overset{\rightarrow} {{j}} \\ $$