What is the greatest length of copper wire that can hang without breaking ? Breaking stress `=7.2xx10^(7)Nm^(-2)`. Density of copper `=7.2 g//c.c.` , `g=10 ms^(-2)`

Options

A. `100 m`
B. `1000 m`
C. `150 m`
D. `1500 m`

Explanation

To determine the greatest length of copper wire that can hang without breaking, we can use the relationship between breaking stress, density, and gravitational force. Here’s a step-by-step solution:

### Step 1: Understand the Given Information
- Breaking stress (σ) = \(7.2 \times 10^7 \, \text{N/m}^2\)
- Density of copper (ρ) = \(7.2 \, \text{g/cm}^3 = 7.2 \times 10^3 \, \text{kg/m}^3\) (conversion from g/cm³ to kg/m³)
- Gravitational acceleration (g) = \(10 \, \text{m/s}^2\)

### Step 2: Use the Formula for Breaking Stress
The breaking stress is defined as the force per unit area. We can express this as:
\[ \sigma = \frac{F}{A} \]
Where:
- \(F\) is the force (weight of the wire)
- \(A\) is the cross-sectional area of the wire

### Step 3: Calculate the Force (Weight of the Wire)
The weight of the wire can be expressed as:
\[ F = m \cdot g \]
Where:
- \(m\) is the mass of the wire
- \(g\) is the acceleration due to gravity

### Step 4: Express Mass in Terms of Volume and Density
The mass of the wire can also be expressed in terms of its volume and density:
\[ m = V \cdot \rho \]
Where:
- \(V\) is the volume of the wire

### Step 5: Volume of the Wire
Assuming the wire has a uniform cross-section, the volume \(V\) can be expressed as:
\[ V = A \cdot L \]
Where:
- \(L\) is the length of the wire

### Step 6: Substitute Mass into the Force Equation
Substituting the expression for mass into the force equation gives:
\[ F = (A \cdot L) \cdot \rho \cdot g \]

### Step 7: Substitute Force into the Breaking Stress Equation
Now, substituting \(F\) into the breaking stress formula:
\[ \sigma = \frac{(A \cdot L) \cdot \rho \cdot g}{A} \]
This simplifies to:
\[ \sigma = L \cdot \rho \cdot g \]

### Step 8: Solve for Length (L)
Rearranging the equation to solve for \(L\):
\[ L = \frac{\sigma}{\rho \cdot g} \]

### Step 9: Substitute the Values
Now, substituting the known values into the equation:
\[ L = \frac{7.2 \times 10^7}{7.2 \times 10^3 \cdot 10} \]

### Step 10: Calculate the Length
Calculating the right-hand side:
\[ L = \frac{7.2 \times 10^7}{7.2 \times 10^4} = 10^3 \, \text{m} = 1000 \, \text{m} \]

### Conclusion
The greatest length of copper wire that can hang without breaking is **1000 meters**.

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