A disk of radius R and density o(r) = 0,(1 –-). A semi-circular disk of uniform density and radius R. y R
A disk of radius R and density o(r) = 0,(1 –-). A semi-circular disk of uniform density and radius R. y R
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![### Description of the Disk
The image describes a disk with a radius \( R \) and a radial density distribution given by:
\[ \sigma(r) = \sigma_0 \left(1 - \frac{r}{R}\right) \]
### Explanation of the Diagram
The diagram shows a semi-circular disk with uniform density and a radius labeled \( R \). It is situated in a coordinate system with the semicircle resting on the x-axis and centered on the y-axis.
- **Axes:**
- The x-axis is horizontal.
- The y-axis is vertical.
- **Disk:**
- The semicircle extends from the y-axis outward to the edge of the circle, forming a half-disk shape above the x-axis.
- The radius \( R \) extends from the center (origin) to any point along the boundary of the semicircle.
The density function represents how the density of the disk changes with distance \( r \) from the center. As \( r \) approaches \( R \), the density decreases linearly from \( \sigma_0 \) to zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b937620-31e5-470f-b146-f538889220b0%2F06f0ad0e-ce9b-4564-9198-cb722de332a1%2F795jdh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Description of the Disk
The image describes a disk with a radius \( R \) and a radial density distribution given by:
\[ \sigma(r) = \sigma_0 \left(1 - \frac{r}{R}\right) \]
### Explanation of the Diagram
The diagram shows a semi-circular disk with uniform density and a radius labeled \( R \). It is situated in a coordinate system with the semicircle resting on the x-axis and centered on the y-axis.
- **Axes:**
- The x-axis is horizontal.
- The y-axis is vertical.
- **Disk:**
- The semicircle extends from the y-axis outward to the edge of the circle, forming a half-disk shape above the x-axis.
- The radius \( R \) extends from the center (origin) to any point along the boundary of the semicircle.
The density function represents how the density of the disk changes with distance \( r \) from the center. As \( r \) approaches \( R \), the density decreases linearly from \( \sigma_0 \) to zero.
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