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 $(x, y, z) = (\frac{4}{3}, 0, 0)$ .

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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.

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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

Electric Charge Field and Potential

Modern Physics

Electricity

Particle Model of Matter

Solid State Physics

Energy Physics

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.