Question

A square lamina of side $a$ and a circular lamina of diameter $a$ are placed touching each other as shown figure. Find distance of their centre of mass from point $O$, the centre of square.

Answer 1

R.E.F image

For unfrom masses, the center of man and the centroid coincide

as continues of figure :-

$x_1=0$ $x_2=3a/2$ $y_1=y_2=0$

and areas :-

$A_1=a^2$ $A_2=\pi a^2$

Centroid of composite figure,

$G=(\frac{A_1{x}_1+A_2{x}_2}{A_1+A_2},\frac{A_2{y}_1+A_2+y_2}{A_1+A_2})$ $\therefore$ distance of center of mass

$=(\frac{0+\frac{3a}{2}\times \pi a^2}{a^2+\pi a^2},0)=(\frac{3a\pi }{1+\pi },0)$ $[d=\frac{3a\pi }{1+\pi }]$