A steel rod has a radius of cross-sectional area is R= 10 mm and length L = 90 cm ls fixed at one end, a force `F = 3.14 * 10^4 N` stretches it along its length, the stress in the rod is equal to (take `pi` = 3.14)

Options

A. `10^8 N/m^2`
B. `3.14* 10^-5 N/m^2`
C. `10^4 N/m^2`
D. `3.14* 10^-4 N/m^2`

Answer

To find the stress in the steel rod, we can use the formula for stress, which is defined as the force applied per unit area. The formula is given by:

\[ \text{Stress} = \frac{\text{Force}}{\text{Area}} \]

### Step 1: Identify the given values
- Radius of the rod, \( r = 10 \, \text{mm} = 10 \times 10^{-3} \, \text{m} \)
- Force applied, \( F = 3.14 \times 10^4 \, \text{N} \)

### Step 2: Calculate the cross-sectional area of the rod
The cross-sectional area \( A \) of a circular rod is given by the formula:

\[ A = \pi r^2 \]

Substituting the values, we have:

\[ A = 3.14 \times (10 \times 10^{-3})^2 \]

Calculating \( (10 \times 10^{-3})^2 \):

\[ (10 \times 10^{-3})^2 = 100 \times 10^{-6} = 10^{-4} \, \text{m}^2 \]

Now substituting back into the area formula:

\[ A = 3.14 \times 10^{-4} \, \text{m}^2 \]

### Step 3: Substitute the values into the stress formula
Now we can calculate the stress:

\[ \text{Stress} = \frac{F}{A} = \frac{3.14 \times 10^4 \, \text{N}}{3.14 \times 10^{-4} \, \text{m}^2} \]

### Step 4: Simplify the expression
The \( 3.14 \) in the numerator and denominator cancels out:

\[ \text{Stress} = \frac{10^4}{10^{-4}} = 10^{4 - (-4)} = 10^{4 + 4} = 10^8 \, \text{N/m}^2 \]

### Step 5: Write the final answer
Thus, the stress in the rod is:

\[ \text{Stress} = 10^8 \, \text{N/m}^2 \]