Half of the rectangular plate shown in figure is made of a material of density ${\mathrm{\rho }}_1$ and the other half of density ${\mathrm{\rho }}_2$. The length of the plate is L. The centre of mass of the system from O is

• A

  $\frac{\mathrm{L}}{2}$

• B

  $\frac{({\mathrm{\rho }}_1+3{\mathrm{\rho }}_2)}{4({\mathrm{\rho }}_1+{\mathrm{\rho }}_2)}\mathrm{L}$

• C

  $\frac{(3{\mathrm{\rho }}_1+{\mathrm{\rho }}_2)}{({\mathrm{\rho }}_1+{\mathrm{\rho }}_2)}\mathrm{L}$

• D

  $\mathrm{Mx} = \mathrm{m}(\mathrm{L} \cos \mathrm{\theta }-\mathrm{x})$