A square plate of edge d and a circular disc of diameter d are placed touching each other at the midpoint of san edge of the plate . Locate the centre of mass of the combination assuming same mass per unit area for the two plates.

Explanation

Let m be the mass per unit area.
`:.` Mass of the square plate `=M_1=d^2/m`
`Mass of the of circular disc =M_2=(pid)^2/4m`
Let the centre of the circular disc be the origin of the system.
`:. x_=d,y_1=0`
`x_2=0,y_2=0`
:. Position of centre of mass
`=((d^2md+pi(d^2/4)mxx0)/(d^2m+pi(d^2/4)m),(0+0)/(m_1+m_2))`
=((d^3m)/(d^2m(1+pi/4),0)`
`=((4d)/(pi+4),0)`
The new centre of mass is `(4d)/((pi+4))` right to the centre of circular disc.