An external force of 20 N acts at an angle of `60^(@)`, with the normal to the surface of a square plate having each side of length 20 cm. What is the stress produced in the plate ?

Options

A. `100N//m^(2)`
B. `150 N//m^(2)`
C. `200N//m^(2)`
D. `250N//m^(2)`

Explanation

To solve the problem, we need to calculate the stress produced in the square plate due to the applied force. Here are the steps to find the solution:

### Step 1: Identify the given values
- External force (F) = 20 N
- Angle with the normal (θ) = 60°
- Length of each side of the square plate (A) = 20 cm = 0.2 m

### Step 2: Calculate the area of the square plate
The area (A) of the square plate can be calculated using the formula:
\[ A = \text{side}^2 = (0.2 \, \text{m})^2 = 0.04 \, \text{m}^2 \]

### Step 3: Resolve the force into components
The force can be resolved into two components:
1. The component acting normal to the surface (F_normal) is given by:
\[ F_{\text{normal}} = F \cdot \cos(θ) = 20 \, \text{N} \cdot \cos(60°) \]
Since \(\cos(60°) = \frac{1}{2}\):
\[ F_{\text{normal}} = 20 \, \text{N} \cdot \frac{1}{2} = 10 \, \text{N} \]

### Step 4: Calculate the stress
Stress (σ) is defined as the force per unit area. The stress produced in the plate due to the normal component of the force is given by:
\[ σ = \frac{F_{\text{normal}}}{A} = \frac{10 \, \text{N}}{0.04 \, \text{m}^2} \]
Calculating this gives:
\[ σ = 250 \, \text{N/m}^2 \]

### Final Answer
The stress produced in the plate is:
\[ \text{Stress} = 250 \, \text{N/m}^2 \]

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