Two forces 25 N and 16 N act on a body of mass 1.0 kg. The minimum acceleration will be

Options

A. `25 ms ^(-2)`
B. `16 ms ^(-2)`
C. `9 ms ^(-2)`
D. `41 ms ^(-2)`

Explanation

To find the minimum acceleration of a body acted upon by two forces of 25 N and 16 N, we can follow these steps:

### Step 1: Understand the Forces Acting on the Body
We have two forces acting on a body:
- Force 1 (F1) = 25 N
- Force 2 (F2) = 16 N

### Step 2: Determine the Condition for Minimum Acceleration
The minimum acceleration occurs when the forces are acting in opposite directions. In this case, one force will oppose the other, leading to a resultant force that is the difference between the two forces.

### Step 3: Calculate the Resultant Force
When the forces are in opposite directions, the resultant force (F_res) can be calculated as:
\[ F_{res} = F_1 - F_2 \]
Substituting the values:
\[ F_{res} = 25 \, \text{N} - 16 \, \text{N} = 9 \, \text{N} \]

### Step 4: Apply Newton's Second Law
According to Newton's second law, the acceleration (a) can be calculated using the formula:
\[ a = \frac{F_{res}}{m} \]
where \( m \) is the mass of the body.

### Step 5: Substitute the Values
Given that the mass (m) of the body is 1.0 kg, we can substitute the values into the equation:
\[ a = \frac{9 \, \text{N}}{1.0 \, \text{kg}} = 9 \, \text{m/s}^2 \]

### Final Answer
The minimum acceleration of the body is:
\[ \boxed{9 \, \text{m/s}^2} \]

---