a semicircular disc of redius r remove from rectangular plate of leanth of f and 2r find the com with respect to origin ?

The formula for center of mass:
The x co-ordinate = (m1x1 + m2x2 ..... ) / (m1 + m2 ..... )
The y co-ordinate = (m1y1 + m2y2 ..... ) / (m1 + m2 ..... )
We can say that there are 5 main points:
(0,0), (0,r), (r,r), (2r,r) and (2r,0)
They form the rectangle with a semicircle cut from it in respect with the origin
we can assume the mass of the rectangle to be spread out evenly and that the mass at a point to be x.
Now let's calculate the coordinates for the center of mass:
x coordinate = (0 + 0 + rx + 2rx + 2rx) / (5x)
= 5rx / 5x
= r
y coordinate = (0 + rx + rx + rx + 0 ) / (5x)
= 3rx / 5x
= 3r/5
Thus the center of mass is outside the body at the coordinates (r,3r/5)

 

Regards

Arun (askIITians forum expert)