using the theorem of Pappus ...
let = semicircle fixed radius
= axis of area rotation
let point A be 0 ...
A uniform semicircular lamina has mass M. A is the mid-point of the diameter and B is on the circumference at the other end of the axis of symmetry. A particle of mass m is attached to the lamina at B. The centre of mass of the loaded lamina is at the mid-point of AB. Find in terms of pi, the ratio M:m
The answer given is 3pi : (3pi-8)