Chapter 5: Q22P (page 257)

In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ ,
find:
The centroid of the volume.

Short Answer

Expert verified

The centroid of the volume is $(x, y, z) = (\frac{4}{3}, 0, 0)$ .

Step by step solution

Definition of Centroid of volume

The geometric center of a particular body having a specific shape is known as the centroid of volume. In the case of uniform density, the center of mass lies on the centroid of volume, and also the center of gravity lies on it.

Representation of the area bounded by the curve

Draw the bounded region for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ .

Step 3: Calculation of the value of x

If the surface be rotated around the x- axis, then only $x$ remains, and $y = z = 0$ .

$x = \frac{1}{V} \int_{0}^{2} π {(f (x))}^{2} xdx = \frac{1}{2 π} \int_{0}^{2} {πx}^{2} xdx {= \frac{1}{6} x^{3}}_{0}^{2} = \frac{4}{3}$

Thus, the centroid of the volume $(x, y, z) = (\frac{4}{3}, 0, 0)$ .

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.

In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ ,
find:
The centroid of the volume.

Short Answer

Step by step solution

Definition of Centroid of volume

Representation of the area bounded by the curve

Step 3: Calculation of the value of x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Work Energy and Power

Force

Wave Optics

Fluids

Electrostatics

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.

In Problems 17 to 30, for the curve y=x, betweenx=0andx=2,find:The centroid of the volume.

Short Answer

Step by step solution

Definition of Centroid of volume

Representation of the area bounded by the curve

Step 3: Calculation of the value of x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Work Energy and Power

Force

Wave Optics

Fluids

Electrostatics

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.

In Problems 17 to 30, for the curve $y = \sqrt{x}$ , between $x = 0$ and $x = 2$ ,
find:
The centroid of the volume.