Two long metallic strips are joined together by two rivets each of radius `2 mm`. Each rivet can withstand a maximum shearing stress of `1.5 xx 10^(9) N//m^(2)`. Assuming that each rivet shares the stretching load equally, the maximum tensile force the strip can exert without rupture is

Options

A. `1.88xx10^(4)N`
B. `3.8xx10^(4)N`
C. `6xx10^(7)N`
D. `3xx10^(4)N`

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Identify the given values
- Radius of each rivet, \( r = 2 \, \text{mm} = 2 \times 10^{-3} \, \text{m} \)
- Maximum shearing stress, \( \sigma = 1.5 \times 10^{9} \, \text{N/m}^2 \)

### Step 2: Calculate the cross-sectional area of one rivet
The area \( A \) of a circular rivet can be calculated using the formula:
\[ A = \pi r^2 \]
Substituting the radius into the formula:
\[ A = \pi (2 \times 10^{-3})^2 = \pi (4 \times 10^{-6}) \approx 1.25664 \times 10^{-5} \, \text{m}^2 \]

### Step 3: Relate shearing stress to force
The maximum shearing stress is defined as:
\[ \sigma = \frac{F}{A} \]
Where \( F \) is the force acting on one rivet. Rearranging this formula gives:
\[ F = \sigma \cdot A \]

### Step 4: Substitute the values to find the force on one rivet
Now substituting the values of \( \sigma \) and \( A \):
\[ F = (1.5 \times 10^{9}) \cdot (1.25664 \times 10^{-5}) \approx 18850.1 \, \text{N} \]
This means the maximum tensile force that one rivet can withstand is approximately \( 18850.1 \, \text{N} \).

### Step 5: Calculate the total force for two rivets
Since there are two rivets sharing the load equally, the total maximum tensile force \( F_{total} \) that the strips can exert without rupture is:
\[ F_{total} = 2 \cdot F = 2 \cdot 18850.1 \approx 37700.2 \, \text{N} \]

### Step 6: Convert to kilonewtons
To express the total force in kilonewtons:
\[ F_{total} \approx 37.7 \, \text{kN} \]

### Final Answer
The maximum tensile force the strip can exert without rupture is approximately \( 37.7 \, \text{kN} \).

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