The figure shows a square metal plate of side `l` from which a square plate of side a has been cut as shown in the figure. Find the ratio `(a//l)` so that the centre of mass of the remaining L-shaped plate coincides with the point A

Answer

`((sqrt5 - 1)/(2))`

Explanation

`vec(y) = ((rhol^(2)) xx (l)/(2) - (rhoa^(2))(a)/(2))/(rhol^(2) - rhoa^(2)) = a rArr l^(2) - al - a^(2) = 0`
`rArr a = ((sqrt5 - 1)l)/(2) x`