A thin sheet of metal of uniform thckness is cut into the shape bounded by the line `x = a` and `y = +- kx^(2)`, as shown. Find the coordinates of the centre of mass

Answer

`x = (3a)/(4)`

Explanation

`x_(cm) = (int xdm)/(int dm) = (int_(0)^(a) xrhoydx)/(int_(0)^(a) rhoydx) = (3)/(4)a`