Two blocks with masses `m_(1) = 0.2` kg and `m_(2) = 0.3` kg hang one under other as shown in figure. Find the tensions in the strings (massless) in the following situations :
`(g = 10 m//s^(2))`
the blocks are at rest

Explanation

To solve the problem of finding the tensions in the strings when the blocks are at rest, we will analyze the forces acting on each block separately.

### Step-by-Step Solution:

1. **Identify the Masses and Gravitational Force**:
- Mass of block 1, \( m_1 = 0.2 \) kg
- Mass of block 2, \( m_2 = 0.3 \) kg
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

2. **Calculate the Weight of Each Block**:
- Weight of block 1, \( W_1 = m_1 \cdot g = 0.2 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 2 \, \text{N} \)
- Weight of block 2, \( W_2 = m_2 \cdot g = 0.3 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 3 \, \text{N} \)

3. **Analyze the Forces on Block 2**:
- Let \( T_2 \) be the tension in the string supporting block 2.
- Since block 2 is at rest, the forces acting on it are balanced:
\[ T_2 = W_2 \]
- Therefore, substituting the weight of block 2:
\[ T_2 = 3 \, \text{N} \]

4. **Analyze the Forces on Block 1**:
- Let \( T_1 \) be the tension in the string supporting block 1.
- The forces acting on block 1 are the tension \( T_1 \) upwards and the combined weight of block 2 and its own weight downwards:
\[ T_1 = T_2 + W_1 \]
- Substituting the values we have:
\[ T_1 = 3 \, \text{N} + 2 \, \text{N} = 5 \, \text{N} \]

5. **Final Results**:
- The tension in the string supporting block 2 is \( T_2 = 3 \, \text{N} \).
- The tension in the string supporting block 1 is \( T_1 = 5 \, \text{N} \).

### Summary of Tensions:
- \( T_1 = 5 \, \text{N} \)
- \( T_2 = 3 \, \text{N} \)