Find the coordinate of the centroid for the shaded part of the lamina with respect to given reference axis.[Figure: origin O with x-axis to the right and y-axis upward. A semicircle of radius R = 8 cm (the digit is partly obscured in the scan; read a…

Q.2 (A) Find the coordinate of the centroid for the shaded part of the lamina with respect to given reference axis.

[Figure: origin O with x-axis to the right and y-axis upward. A semicircle of radius R = 8 cm (the digit is partly obscured in the scan; read as 8 cm, consistent with the drawing) centred at O lies below the x-axis, spanning x = −8 cm to x = 8 cm. A right-angled triangle lies above the x-axis with one vertex at O, base along the x-axis from O to x = 8 cm, vertical side at x = 8 cm, and hypotenuse from O at 60° to the x-axis. A semicircle of radius r = 3 cm, below the x-axis with its diameter on the x-axis from x = −8 cm to x = −2 cm (centre at (−5, 0)), is cut out. The remaining region (big semicircle + triangle − small semicircle) is shaded.]