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 the force acting on an object is equal to the mass of that object multiplied by its acceleration (F = m * a).

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the lighter body (m1) = 4 kg
- Mass of the heavier body (m2) = 5 kg
- Acceleration of the lighter body (a1) = 2 m/s²

2. **Calculate the Force Acting on the Lighter Body:**
- Using Newton's second law:
\[ F = m_1 \times a_1 \]
- Substitute the values:
\[ F = 4 \, \text{kg} \times 2 \, \text{m/s}^2 = 8 \, \text{N} \]

3. **Determine the Force Acting on the Heavier Body:**
- Since both bodies are acted upon by the same force, the force acting on the heavier body (F) is also 8 N.

4. **Calculate the Acceleration of the Heavier Body:**
- Using Newton's second law again for the heavier body:
\[ F = m_2 \times a_2 \]
- Rearranging the formula to find acceleration:
\[ a_2 = \frac{F}{m_2} \]
- Substitute the values:
\[ a_2 = \frac{8 \, \text{N}}{5 \, \text{kg}} = 1.6 \, \text{m/s}^2 \]

5. **Conclusion:**
- The acceleration of the heavier body (5 kg) is 1.6 m/s².

### Final Answer:
The acceleration of the heavier body is **1.6 m/s²**.

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