A uniform lamina ABCDE is made from a square ABDE and anequilaterial triangle BCD. Find the centre of mass of the lamina.

A uniform lamina ABCDE is made from a square ABDE and anequilaterial t

1.	A uniform lamina ABCDE is made from a square ABDE and anequilaterial triangle BCD. Find the centre of mass of the lamina.
Answer» Solution :Here, `A_(1)`= area of square ABDE =(a)(a) =`a^(2)` `A_(2)` = area of triangle `=1/2(a)((sqrt(3)a)/2) = sqrt(3)/4 a^(2)` `(x_(1),y_(1))` = co-ordiantes of centre of MASS of square `=(a/2,0)` `(x_(2),y_(2))` =co-ordinates of centre of mass of the triangle = `(a + a/(2sqrt(3)),0)` Now, `x_(CM) =(A_(1)x_(1) + A_(2)x_(2))/(A_(1) + A_(2)) =((a^(2)).(a/2) + (sqrt(3)a^(2))/4 (a+a/(2sqrt(3))))/(a^(2) + sqrt(3)/4 a^(2)) = 0.74 a` `Y_(CM) =0` as `y_(1)` and `y_(2)` both are zero. Therefore co-ordinates of CM of the given lamina are (0.74a, 0).