Folosim sistemul cartezian desenat in imaginea data.
Observam ca axa Ox este axa de simetrie a placii.
Asta inseamna ca centrul de greutate se afla pe axa Ox.
Vom calcula doar coordonata x a centrului de greutate.
[tex]\displaystyle\\y_{CG}=0\\\\x_{CG}=\frac{0\cdot a^2-\dfrac{a}{4}\cdot\left(\dfrac{a}{4}\right)^2}{a^2-\left(\dfrac{a}{4}\right)^2}=\frac{-\dfrac{a}{4}\cdot\left(\dfrac{a}{4}\right)^2}{a^2-\left(\dfrac{a}{4}\right)^2}=\frac{-\dfrac{a}{4}\cdot\dfrac{a^2}{4^2}}{a^2-\dfrac{a^2}{4^2}}=\\\\\\=\frac{-\dfrac{a^3}{4^3}}{\dfrac{4^2a^2-a^2}{4^2}}=\frac{-\dfrac{a^3}{4^3}}{\dfrac{4^2a^2-a^2}{4^2}}=\frac{-\dfrac{a^3}{4^3}}{\dfrac{(4^2-1)\cdot~a^2}{4^2}}=\frac{-\dfrac{a^3}{4^3}}{\dfrac{15a^2}{4^2}}=[/tex]
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[tex]\displaystyle\\=\frac{-\dfrac{a^3}{4^3}}{\dfrac{15a^2}{4^2}}=-\frac{a^3}{4^3}\cdot \frac{4^2}{15a^2}=-\frac{a}{4}\cdot \frac{1}{15}=\boxed{\bf-\frac{a}{60}}\\\\[/tex]
