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

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Famous Physicists

Particle Model of Matter

Atoms and Radioactivity

Kinematics Physics

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.

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

Magnetism

Famous Physicists

Particle Model of Matter

Atoms and Radioactivity

Kinematics Physics

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.

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