Chapter 1: Q9MP (page 1)

Find the centroid of the area above $y = x^{2}$ and below y = c (c > 0).

Short Answer

Expert verified

The centroid $(\bar{x}, \bar{y}) = (\frac{3}{8} c^{\frac{1}{2}}, \frac{3}{5} c)$

Step by step solution

Given values

The values of the centroid is as follows:

$y = x^{2}$ , $y = c (c > 0)$

Concept of area of centroid

When finding the centroid of a two-dimensional shape, looking for both an x and a y coordinate, represented as x̄ and ȳ respectively. Collectively, this x and y coordinate is the centroid of the shape. $c = (\bar{x,} \bar{y})$

Find the area

The value of c must be $c ⩾ 0$ .

Find the area of centroid using the formula,

$A = \int_{0}^{\sqrt{x}} d x \int_{x^{2}}^{c} d y = \int_{0}^{\sqrt{c}} d x (c - x^{2})$

role="math" localid="1664232091282" $= [c x - \frac{1}{3} x^{3}] | 0^{\sqrt{c}}$

$= \frac{2}{3} c^{\frac{3}{2}}$

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Find the centroid of the area above $y = x^{2}$ and below y = c (c > 0).

Short Answer

Step by step solution

Given values

Concept of area of centroid

Find the area

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Find the centroid of the area abovey=x2and below y = c (c > 0).

Short Answer

Step by step solution

Given values

Concept of area of centroid

Find the area

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Kinematics Physics

Wave Optics

Classical Mechanics

Fundamentals of Physics

Force

Electricity

Study anywhere. Anytime. Across all devices.

Find the centroid of the area above $y = x^{2}$ and below y = c (c > 0).