Two blocks of masses 2 kg and 1 kg are placed on a smooth horizontal table in contact with each other. A horizontal force of 3 newton is applied on the first so that the block moves with a constant acceleration. The force between the blocks would be

Options

A. 3 newton
B. 2 newton
C. 1 newton
D. zero

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the System
We have two blocks on a smooth horizontal table:
- Block 1 (mass \( m_1 = 2 \, \text{kg} \))
- Block 2 (mass \( m_2 = 1 \, \text{kg} \))

A horizontal force \( F = 3 \, \text{N} \) is applied to Block 1.

### Step 2: Calculate the Total Mass
The total mass of the system (both blocks) is:
\[ m_{\text{total}} = m_1 + m_2 = 2 \, \text{kg} + 1 \, \text{kg} = 3 \, \text{kg} \]

### Step 3: Calculate the Acceleration of the System
Using Newton's second law, the acceleration \( a \) of the system can be calculated as:
\[ F = m_{\text{total}} \cdot a \implies a = \frac{F}{m_{\text{total}}} = \frac{3 \, \text{N}}{3 \, \text{kg}} = 1 \, \text{m/s}^2 \]

### Step 4: Analyze the Forces Acting on Block 2
Block 2 (1 kg) is in contact with Block 1 and will experience a force due to the acceleration of the system. The force \( F_{12} \) that Block 1 exerts on Block 2 can be calculated using:
\[ F_{12} = m_2 \cdot a = 1 \, \text{kg} \cdot 1 \, \text{m/s}^2 = 1 \, \text{N} \]

### Step 5: Conclusion
The force between the two blocks is \( 1 \, \text{N} \).

### Final Answer
The force between the blocks is \( 1 \, \text{N} \).

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