Half of the recrtangular plate shown in figure is made of a material of density `rho_1` and the other half of density `rho_2`. The length of the plate is L. Locate the centre of mass of the plate.

Options

A. `(L)/(2)`
B. `((rho_1 + 3 rho_2))/(4(rho_1 + rho_2))L`
C. `((3 rho_1 + rho_2))/((rho_1 + rho_2))L`
D. `Mx = m(L cos theta - x)`

Answer

B

Explanation

(b) Let area of each half is `A` and thickness of the plane is `t`
mass of left half `= m_1 = rho_1` At, `x_1 = (L)/(4)`
`"mass of right half" = m_2 = rho_2` At, `x_2 = (3 L)/(4)`
Now apply `x_(cm) = (m_1 x_1 + m_2 x_2)/(m_1 + m_2) =(P_1 L + 3 P_2 L)/(4(P_1 + P_2))`.