The center of mass of a thin rectangular plate (fig - x ) with sides of length a and b, whose mass per unit area $$(\sigma)$$ varies as

$$\sigma = \frac{\sigma_{\circ}x}{ab}$$ (where $$\sigma_{\circ}$$ is a constant), would be

A

$$\left(\frac{2}{3}a,\frac{b}{2}\right)$$

B

$$\left(\frac{a}{2},\frac{b}{2}\right)$$

C

$$\left(\frac{1}{3}a,\frac{b}{2}\right)$$

D

$$\left(\frac{2}{3}a,\frac{2}{3}b\right)$$