Find the stress in CD. Area of CD = 2 m² A B C D 40N 15 N/m² 5 N/m² 20 N/m² A None of these C B 10N D E F 30N D

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### Problem Statement

Find the stress in CD.  
Area of CD = \( 2 \, m^2 \)

#### Diagram
The diagram depicts two rectangular blocks with various forces acting on them:

- A rectangle is labeled with points A to F, marking its boundaries.
- There are two forces acting towards the left side: 
  - A force of 40 N at point A.
  - A force of 10 N at point C.
- There are two forces acting towards the right side:
  - A force of 30 N at point F.
  
### Options

A. \( 15 \, N/m^2 \)  
B. \( 5 \, N/m^2 \)  
C. \( 20 \, N/m^2 \)  
D. None of these

#### Explanation of Diagram:
The diagram shows a system in equilibrium with forces distributed along a line through the blocks at points labeled A, B, C, D, E, and F. The forces are as follows:

- 40N force at point A, directed left.
- 10N force between points C and D, directed left.
- 30N force at point F, directed right.

The objective is to find the stress in the section CD, which has an area of \( 2 \, m^2 \).

#### Steps for Calculation:
1. **Determine Net Force in CD:**

   The net force acting on CD can be calculated by analyzing the internal force distribution. Assume equilibrium for section CD:
   
   Net Force in CD = \( 40N - 10N - 30N \) 
                   = \( 0N \)

2. **Calculate Stress:**

   Stress is given by the formula:
   
   \( \sigma = \frac{F}{A} \)
   
   where \( F \) is the force and \( A \) is the area.
   
   Substitute the values:
   
   \( \sigma = \frac{0N}{2 \, m^2} \) 
           = \( 0 \, N/m^2 \)

   As the net force is 0, the correct option is \( \text{None of these} \).

Hence, the correct answer is:
D. None of these
Transcribed Image Text:### Problem Statement Find the stress in CD. Area of CD = \( 2 \, m^2 \) #### Diagram The diagram depicts two rectangular blocks with various forces acting on them: - A rectangle is labeled with points A to F, marking its boundaries. - There are two forces acting towards the left side: - A force of 40 N at point A. - A force of 10 N at point C. - There are two forces acting towards the right side: - A force of 30 N at point F. ### Options A. \( 15 \, N/m^2 \) B. \( 5 \, N/m^2 \) C. \( 20 \, N/m^2 \) D. None of these #### Explanation of Diagram: The diagram shows a system in equilibrium with forces distributed along a line through the blocks at points labeled A, B, C, D, E, and F. The forces are as follows: - 40N force at point A, directed left. - 10N force between points C and D, directed left. - 30N force at point F, directed right. The objective is to find the stress in the section CD, which has an area of \( 2 \, m^2 \). #### Steps for Calculation: 1. **Determine Net Force in CD:** The net force acting on CD can be calculated by analyzing the internal force distribution. Assume equilibrium for section CD: Net Force in CD = \( 40N - 10N - 30N \) = \( 0N \) 2. **Calculate Stress:** Stress is given by the formula: \( \sigma = \frac{F}{A} \) where \( F \) is the force and \( A \) is the area. Substitute the values: \( \sigma = \frac{0N}{2 \, m^2} \) = \( 0 \, N/m^2 \) As the net force is 0, the correct option is \( \text{None of these} \). Hence, the correct answer is: D. None of these
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