Question

what is the centre of gravity of a semi circle is at a perpendicular distance from its centre
1.3r/4pie
2.4r/3pie
3.8r/3
4.3r/8​

Answer 1

The center of gravity of a semi circle is at a perpendicular distance from its center is 2. 4r/3π

Step-by-step explanation:

Now, the point (x, y) is:

x = ∫x.dA/A

And

y = ∫y.dA/A = ∫(y/2 (y.dx))/(1/2 πR²)

y = ∫ y² dx/πR²

$y=2\int_{R}^{0}\left ( R^2-x^2 \right )dx/\pi R^2$

$y=2\left [ R^2x -x^3/3 \right ]^R_0/\pi R^2$

y = 2[R³ - R³/2]/πR²

y = 2(2/3 R³)/πR²

∴ y = 4R/3π

The perpendicular distance from center of semicircle is y axis. Thus, the center of gravity is at 4R/3π from center.