From a circular plate of diameter 6.0 cm a circle is cut out whose diameter is a radius of the plate. The distance of center of gravity of the remainder from the center of circular plate is
From a circular plate of diameter 6.0 cm a circle is cut out whose diameter is a radius of the plate. The distance of center of gravity of the remainder from the center of circular plate is
Chapter2: Loads On Structures
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![### Example Problem: Finding the Center of Gravity of a Cut Plate
From a circular plate of diameter 6.0 cm, a circle is cut out whose diameter is a radius of the plate. The distance of the center of gravity of the remainder from the center of the circular plate is
(a) *Provide multiple choice options if available*
### Explanation:
1. **Initial Setup**:
- The circular plate has a diameter of 6.0 cm.
- A smaller circle, whose diameter is equal to the radius of the original plate, is cut out.
2. **Calculation Steps**:
- Original plate diameter, D = 6.0 cm.
- Radius, R = D/2 = 6.0 cm / 2 = 3.0 cm.
- The cut-out circle has a diameter equal to this radius, so its diameter = 3.0 cm and its radius = 3.0 cm / 2 = 1.5 cm.
3. **Center of Gravity Calculation**:
- We need to find the distance of the center of gravity of the remaining portion from the center of the original plate.
- Let the coordinates of the center of the original circular plate be (0,0).
- When a circle is cut out, the remaining part's center of gravity (C) shifts towards the opposite direction of the cut-out circular center.
- Using the principle of moments, the new center of gravity can be determined.
### Detailed Steps:
- If the center of the cut-out circle is at distance R (3.0 cm) from the center of the original plate on the x-axis, the remaining mass of the plate shifts accordingly.
- The distance from the original center to the new center of gravity:
\[
\text{{Distance}} = \frac{{\text{{radius of plate}} - (\text{{radius of small circle}})^2}}{{\text{{radius of plate}}}} = \frac{{3 - 1.5}}{{3}} = 1.5 \text{ cm}
\]
### Conclusion:
The distance of the center of gravity of the remaining part of the circular plate from the center of the original circular plate is 1.5 cm. This calculation helps understand how the removal of a portion affects the center of gravity in a uniform plate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55d52e12-5d83-4118-bfcc-903cc074d889%2F71203f26-8dbb-4b04-8eb7-1f9a614c83dd%2F918ivr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Problem: Finding the Center of Gravity of a Cut Plate
From a circular plate of diameter 6.0 cm, a circle is cut out whose diameter is a radius of the plate. The distance of the center of gravity of the remainder from the center of the circular plate is
(a) *Provide multiple choice options if available*
### Explanation:
1. **Initial Setup**:
- The circular plate has a diameter of 6.0 cm.
- A smaller circle, whose diameter is equal to the radius of the original plate, is cut out.
2. **Calculation Steps**:
- Original plate diameter, D = 6.0 cm.
- Radius, R = D/2 = 6.0 cm / 2 = 3.0 cm.
- The cut-out circle has a diameter equal to this radius, so its diameter = 3.0 cm and its radius = 3.0 cm / 2 = 1.5 cm.
3. **Center of Gravity Calculation**:
- We need to find the distance of the center of gravity of the remaining portion from the center of the original plate.
- Let the coordinates of the center of the original circular plate be (0,0).
- When a circle is cut out, the remaining part's center of gravity (C) shifts towards the opposite direction of the cut-out circular center.
- Using the principle of moments, the new center of gravity can be determined.
### Detailed Steps:
- If the center of the cut-out circle is at distance R (3.0 cm) from the center of the original plate on the x-axis, the remaining mass of the plate shifts accordingly.
- The distance from the original center to the new center of gravity:
\[
\text{{Distance}} = \frac{{\text{{radius of plate}} - (\text{{radius of small circle}})^2}}{{\text{{radius of plate}}}} = \frac{{3 - 1.5}}{{3}} = 1.5 \text{ cm}
\]
### Conclusion:
The distance of the center of gravity of the remaining part of the circular plate from the center of the original circular plate is 1.5 cm. This calculation helps understand how the removal of a portion affects the center of gravity in a uniform plate.
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