When a same force is applied on two different objects. It produces accelerations of `4m/sec^(2)` and `6m/sec^(2)`. In these objects, if the same force is applied on the combination of these objects, calculate acceleration of combination.

Answer

To solve the problem, we need to find the acceleration of the combination of two objects when the same force is applied to both of them. Let's break it down step by step.

### Step 1: Understand the Given Information
We have two objects with accelerations:
- Object 1 has an acceleration \( a_1 = 4 \, \text{m/s}^2 \)
- Object 2 has an acceleration \( a_2 = 6 \, \text{m/s}^2 \)

The same force \( F \) is applied to both objects.

### Step 2: Relate Force, Mass, and Acceleration
Using Newton's second law, we can express the force in terms of mass and acceleration:
- For Object 1:
\[ F = m_1 \cdot a_1 \]
- For Object 2:
\[ F = m_2 \cdot a_2 \]

From these equations, we can express the masses \( m_1 \) and \( m_2 \) in terms of the force \( F \):
- \( m_1 = \frac{F}{a_1} \)
- \( m_2 = \frac{F}{a_2} \)

### Step 3: Combine the Masses
The total mass of the combination of the two objects is:
\[ m_{\text{total}} = m_1 + m_2 = \frac{F}{a_1} + \frac{F}{a_2} \]

### Step 4: Factor Out the Force
We can factor out \( F \):
\[ m_{\text{total}} = F \left( \frac{1}{a_1} + \frac{1}{a_2} \right) \]

### Step 5: Find the Acceleration of the Combination
When the same force \( F \) is applied to the combined mass, we can write:
\[ F = m_{\text{total}} \cdot a \]
Substituting for \( m_{\text{total}} \):
\[ F = F \left( \frac{1}{a_1} + \frac{1}{a_2} \right) \cdot a \]

### Step 6: Cancel the Force
Since \( F \) is common on both sides, we can cancel it out (assuming \( F \neq 0 \)):
\[ 1 = \left( \frac{1}{a_1} + \frac{1}{a_2} \right) \cdot a \]

### Step 7: Solve for Acceleration \( a \)
Rearranging gives us:
\[ a = \frac{1}{\frac{1}{a_1} + \frac{1}{a_2}} \]

### Step 8: Substitute the Values
Now substituting the values of \( a_1 \) and \( a_2 \):
\[ a = \frac{1}{\frac{1}{4} + \frac{1}{6}} \]

### Step 9: Calculate the Denominator
Finding a common denominator (which is 12):
\[ \frac{1}{4} = \frac{3}{12}, \quad \frac{1}{6} = \frac{2}{12} \]
Thus,
\[ \frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12} \]

### Step 10: Final Calculation
Now substituting back:
\[ a = \frac{1}{\frac{5}{12}} = \frac{12}{5} = 2.4 \, \text{m/s}^2 \]

### Final Answer
The acceleration of the combination is:
\[ \boxed{2.4 \, \text{m/s}^2} \]