Answer to Question #259440 in Mechanics | Relativity for Karthi

Question

Q1. For the shaded area shown in figure. Determine:-Co-ordinates of centroid

The removed area is semi-circle and all the given dimensions are in cm. Dimension of rectangle is 12.5*20 cm² and diameter of semi-circle is 7.5 cm.

12.5

7.5

Answer 1

The center of mass of the semicircle is

$$x_{cc}=\frac{4R}{3\pi}.$$

The center of mass can be found by the center of mass of the rectangle and the semicircle:

$$x_c=\frac{x_{cr}m_r+x_{cc}m_c}{m_r+m_c},\\\space\\ x_c=\frac{(20/2)·(20·12.5)+(20+4·3.75/(3\pi))(\pi ·3.75^2/2))}{20·12.5+\pi ·3.75^2/2},\\\space\\ x_c=10.94\text{ cm}.$$