Question

Question: (1 marks)
The x or y coordinate of the centroid of a
quadrant of a circular area of radius ris
A) 4r/3π
Þ) 2r/3π
1) 2r/π
Dr/π
A
B
C
D
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Answer 1

b

Step-by-step explanation:

i think so but it is not sure answer

Answer 2

Answer:

A) 4r/3\pi

Step-by-step explanation:

Equation of the circle : $x^2+y^2=r^2$, taking small vertical strip of width dx,

$dA = ydx$. then, transforming intregral into r and Ф form we solve.

Formula for centroid of any 2-D space is given by

$\bar x=\frac{\int x\, dA}{\int dA} \\\\\bar x =\frac{\int\limits^{\pi/2}_0 { \frac{r^3}{3}cos\theta d\theta \,} }{\int\limits^{\pi/2}_0 { \frac{r^2}{2} d\theta}} \\\\\\\bar x = \frac{2r}{3} \frac{1}{\pi/2} =\frac{4r}{3\pi}$