Two bodies of masses 2 kg and 3 kg are connected by a metal wire of cross-section 0.04 `mm^(2)` and are placed on a frictionless horizontal surface. Breaking stress of metal wire is 2.5 Gpa. The maximum force F that can be applied to 3kg block so that wire does not break is

Options

A. 100 N
B. 150 N
C. 200 N
D. 250 N

Explanation

To solve the problem, we need to determine the maximum force \( F \) that can be applied to the 3 kg block without breaking the metal wire connecting it to the 2 kg block.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of block 1, \( m_1 = 2 \, \text{kg} \)
- Mass of block 2, \( m_2 = 3 \, \text{kg} \)
- Cross-sectional area of the wire, \( A = 0.04 \, \text{mm}^2 = 0.04 \times 10^{-6} \, \text{m}^2 = 4 \times 10^{-8} \, \text{m}^2 \)
- Breaking stress of the wire, \( \sigma = 2.5 \, \text{GPa} = 2.5 \times 10^9 \, \text{Pa} \)

2. **Calculate the Maximum Tension (T) in the Wire:**
- The maximum tension in the wire can be calculated using the formula for stress:
\[ \sigma = \frac{T}{A} \]
- Rearranging for \( T \):
\[ T = \sigma \times A \]
- Substituting the values:
\[ T = (2.5 \times 10^9 \, \text{Pa}) \times (4 \times 10^{-8} \, \text{m}^2) = 100 \, \text{N} \]

3. **Relate Tension to the Applied Force (F):**
- When a force \( F \) is applied to the 3 kg block, both blocks will accelerate together. The acceleration \( a \) can be expressed as:
\[ a = \frac{F}{m_1 + m_2} = \frac{F}{2 + 3} = \frac{F}{5} \]
- The tension in the wire (which is the force acting on the 2 kg block) can be expressed as:
\[ T = m_1 \cdot a = 2 \cdot a = 2 \cdot \frac{F}{5} = \frac{2F}{5} \]

4. **Set the Tension Equal to the Maximum Tension:**
- Since the maximum tension \( T \) we calculated is 100 N, we set up the equation:
\[ \frac{2F}{5} = 100 \]

5. **Solve for the Maximum Force (F):**
- Rearranging the equation gives:
\[ 2F = 100 \times 5 \]
\[ 2F = 500 \]
\[ F = \frac{500}{2} = 250 \, \text{N} \]

### Final Answer:
The maximum force \( F \) that can be applied to the 3 kg block without breaking the wire is **250 N**.