Half of the rectangular plates of length l as shown in the figure is m

1.	Half of the rectangular plates of length l as shown in the figure is made up of a material of density p and other half of density 3p distance of centre of mass from O is
Answer» GIVEN that, Length of half of the PLATES = l Density = ρ Density of half other = 3ρ We need to calculate the MASS of half of rectangular plate Using FORMULA of mass $m_{1}=\rho_{1}\times V_{1}$ Put the value into the formula $m_{1}=\rho\times\dfrac{V}{2}$ We need to calculate the mass of other half of rectangular plate Using formula of mass $m_{2}=\rho_{2}\times V_{2}$ Put the value into the formula $m_{2}=3\rho\times\dfrac{V}{2}$ We need to calculate the CENTER of mass from O Using formula of center of mass $C.M=\dfrac{m_{1}x_{1}+m_{2}x_{2}}{m_{1}+m_{2}}$ Put the value into the formula $C.M=\dfrac{\rho\times\dfrac{V}{2}\times\dfrac{l}{2}+{3\rho\times\dfrac{V}{2}\times\dfrac{l}{2}}}{\rho\times\dfrac{V}{2}+3\rho\times\dfrac{V}{2}}$ $C.M=\dfrac{\rho Vl}{2\rho V}$ $C.M=\dfrac{l}{2}$ Hence, The center of mass from O is $\dfrac{l}{2}$