Two bodies of masses 4 kg and 5kg are acted upon by the same force. If the acceleration of lighter body is `2m//sec^(2)`, then the acceleration of the heavier body is:-

Options

A. `4.2 m//s^(2)`
B. `3.6 m//s^(2)`
C. `2.4 m//s^(2)`
D. `1.6 m//s^(2)`

Explanation

To solve the problem step by step, we will use Newton's second law of motion, which states that \( F = m \cdot a \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.

### Step 1: Identify the given data
- Mass of the lighter body, \( m_1 = 4 \, \text{kg} \)
- Mass of the heavier body, \( m_2 = 5 \, \text{kg} \)
- Acceleration of the lighter body, \( a_1 = 2 \, \text{m/s}^2 \)

### Step 2: Calculate the force acting on the lighter body
Using Newton's second law:
\[ F = m_1 \cdot a_1 \]
Substituting the values:
\[ F = 4 \, \text{kg} \cdot 2 \, \text{m/s}^2 = 8 \, \text{N} \]

### Step 3: Use the same force to find the acceleration of the heavier body
Since the same force acts on both bodies, we can write:
\[ F = m_2 \cdot a_2 \]
Where \( a_2 \) is the acceleration of the heavier body. We already calculated \( F = 8 \, \text{N} \) and we know \( m_2 = 5 \, \text{kg} \). Therefore:
\[ 8 \, \text{N} = 5 \, \text{kg} \cdot a_2 \]

### Step 4: Solve for \( a_2 \)
Rearranging the equation to find \( a_2 \):
\[ a_2 = \frac{8 \, \text{N}}{5 \, \text{kg}} = 1.6 \, \text{m/s}^2 \]

### Final Answer
The acceleration of the heavier body is \( 1.6 \, \text{m/s}^2 \).

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