Question

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 1

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 $\dfrac{l}{2}$