Check my v Consider a uniform right circular cone of specific gravity S < 1, floating with its vertex down in water, S = 1.0. The base radius is R and the cone height is H. Calculate the stability parameter MG of this cone, in dimensionless form.

Structural Analysis
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ISBN:9781337630931
Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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**Problem Statement:**

Consider a uniform right circular cone of specific gravity \( S < 1 \), floating with its vertex down in water, \( S = 1.0 \). The base radius is \( R \) and the cone height is \( H \). Calculate the stability parameter \( MG \) of this cone, in dimensionless form.
Transcribed Image Text:**Problem Statement:** Consider a uniform right circular cone of specific gravity \( S < 1 \), floating with its vertex down in water, \( S = 1.0 \). The base radius is \( R \) and the cone height is \( H \). Calculate the stability parameter \( MG \) of this cone, in dimensionless form.
The image contains a set of multiple-choice questions with four options presented in a mathematical format. All the options represent equations. Here is the detailed transcription of the content in the image:

---

**Question:**

Which of the following equations is correct?

**Options:**

1. (Empty circle selection option)
\[ \frac{MG}{H} = \frac{3}{4} \left( \frac{\zeta \, R^2}{H^2} - 1 + \xi \right) \]

2. (Empty circle selection option)
\[ \frac{MG}{H} = \left( \frac{R^2}{H^2} - 1 + \xi \right) \]

3. (Empty circle selection option)
\[ \frac{MG}{H} = \frac{3}{4} \left( \frac{R^2}{H^2} + 1 + \xi \right) \]

4. (Empty circle selection option)
\[ \frac{MG}{H} = \frac{3}{4} \left( \frac{(\zeta R)^2}{H^2} - 1 + \xi \right) \]

---

For educational purposes, confirm the correct option by simplifying each expression and comparing it with known formulas pertaining to the topic of study.

**Note:** Symbols such as \(\frac{MG}{H}\), \(\zeta\), \(R\), \(H\), and \(\xi\) are typically representative of variables or constants in the given equations, which could be specific to a particular field such as physics or engineering.
Transcribed Image Text:The image contains a set of multiple-choice questions with four options presented in a mathematical format. All the options represent equations. Here is the detailed transcription of the content in the image: --- **Question:** Which of the following equations is correct? **Options:** 1. (Empty circle selection option) \[ \frac{MG}{H} = \frac{3}{4} \left( \frac{\zeta \, R^2}{H^2} - 1 + \xi \right) \] 2. (Empty circle selection option) \[ \frac{MG}{H} = \left( \frac{R^2}{H^2} - 1 + \xi \right) \] 3. (Empty circle selection option) \[ \frac{MG}{H} = \frac{3}{4} \left( \frac{R^2}{H^2} + 1 + \xi \right) \] 4. (Empty circle selection option) \[ \frac{MG}{H} = \frac{3}{4} \left( \frac{(\zeta R)^2}{H^2} - 1 + \xi \right) \] --- For educational purposes, confirm the correct option by simplifying each expression and comparing it with known formulas pertaining to the topic of study. **Note:** Symbols such as \(\frac{MG}{H}\), \(\zeta\), \(R\), \(H\), and \(\xi\) are typically representative of variables or constants in the given equations, which could be specific to a particular field such as physics or engineering.
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