A steel rod has a radius R = 9.5 mm and length L = 81cm. A force `F= 6.2 xx 10^(4)N` stretches it along its length. What is the stress in the rod

Options

A. `0.95 xx 10^(8) N//m^(2)`
B. `1.1 xx 10^(8) N//m^(2)`
C. `2.2 xx 10^(8) N//m^(2)`
D. `3.2 xx 10^(8) Nm^(2)`

Explanation

To find the stress in the steel rod, we can follow these steps:

### Step 1: Understand the formula for stress
Stress (σ) is defined as the force (F) applied per unit area (A) over which the force is distributed. The formula is given by:
\[ \sigma = \frac{F}{A} \]

### Step 2: Calculate the cross-sectional area of the rod
The cross-sectional area (A) of a circular rod can be calculated using the formula:
\[ A = \pi R^2 \]
where R is the radius of the rod.

### Step 3: Convert the radius from mm to meters
The radius is given as R = 9.5 mm. To convert this to meters:
\[ R = 9.5 \, \text{mm} = 9.5 \times 10^{-3} \, \text{m} \]

### Step 4: Calculate the area using the radius
Now, substituting the radius into the area formula:
\[ A = \pi (9.5 \times 10^{-3})^2 \]
Calculating this gives:
\[ A \approx \pi \times (9.5^2 \times 10^{-6}) \approx \pi \times 90.25 \times 10^{-6} \approx 283.53 \times 10^{-6} \, \text{m}^2 \]

### Step 5: Substitute the values into the stress formula
Now we can substitute the values of force and area into the stress formula. The force is given as:
\[ F = 6.2 \times 10^4 \, \text{N} \]
So, substituting these values:
\[ \sigma = \frac{6.2 \times 10^4}{283.53 \times 10^{-6}} \]

### Step 6: Calculate the stress
Calculating the above expression:
\[ \sigma \approx \frac{6.2 \times 10^4}{283.53 \times 10^{-6}} \approx 2.19 \times 10^8 \, \text{N/m}^2 \]

### Final Answer
The stress in the rod is approximately:
\[ \sigma \approx 2.2 \times 10^8 \, \text{N/m}^2 \]

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