A substance breaks down under a stress of `10^(5) Pa`. If the density of the wire is `2 xx 10^(3) kg//m^(3)`, find the minimum length of the wire which will break under its own weight `(g= 10 ms^(-12))`.

Explanation

To find the minimum length of the wire that will break under its own weight, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Breaking Stress**:
The breaking stress (σ) is defined as the force (weight in this case) per unit area (A) that a material can withstand before failing. The formula for breaking stress is given by:
\[ \sigma = \frac{F}{A} \]
where \( F \) is the weight of the wire.

2. **Weight of the Wire**:
The weight (W) of the wire can be expressed as:
\[ W = mg \]
where \( m \) is the mass of the wire and \( g \) is the acceleration due to gravity.

3. **Mass of the Wire**:
The mass of the wire can be calculated using its volume (V) and density (ρ):
\[ m = V \cdot \rho \]
The volume of the wire can be expressed as:
\[ V = A \cdot L \]
where \( L \) is the length of the wire.

4. **Substituting Volume into Mass**:
Therefore, the mass can be rewritten as:
\[ m = A \cdot L \cdot \rho \]

5. **Substituting Mass into Weight**:
Now substituting this expression for mass into the weight formula:
\[ W = (A \cdot L \cdot \rho) \cdot g \]

6. **Substituting Weight into Breaking Stress**:
Now we can substitute the expression for weight into the breaking stress formula:
\[ \sigma = \frac{(A \cdot L \cdot \rho \cdot g)}{A} \]
The area \( A \) cancels out:
\[ \sigma = L \cdot \rho \cdot g \]

7. **Setting Up the Equation**:
According to the problem, the breaking stress is given as \( 10^5 \) Pa. Therefore, we can set up the equation:
\[ 10^5 = L \cdot \rho \cdot g \]

8. **Solving for Length (L)**:
Rearranging the equation to find \( L \):
\[ L = \frac{10^5}{\rho \cdot g} \]

9. **Substituting Values**:
Now substituting the given values: \( \rho = 2 \times 10^3 \, \text{kg/m}^3 \) and \( g = 10 \, \text{m/s}^2 \):
\[ L = \frac{10^5}{(2 \times 10^3) \cdot 10} \]

10. **Calculating Length**:
Simplifying the expression:
\[ L = \frac{10^5}{2 \times 10^4} = \frac{10^5}{2 \times 10^4} = \frac{10}{2} = 5 \, \text{m} \]

### Final Answer:
The minimum length of the wire which will break under its own weight is **5 meters**.