The frictional force of the air on the body of mass 0.25kg, falling with an acceleration of 9.2 `m//s^(2)` will be `(g=9.8m//s^(2))`.

Options

A. 1.0N
B. 0.55N
C. 0.25N
D. 0.15N

Explanation

To solve the problem of finding the frictional force of air on a body of mass 0.25 kg falling with an acceleration of 9.2 m/s², we can follow these steps:

### Step 1: Identify the forces acting on the body
When the body is falling, it experiences two main forces:
- The gravitational force (weight) acting downwards, which is given by \( F_g = mg \).
- The frictional force (air resistance) acting upwards, which we will denote as \( F_f \).

### Step 2: Calculate the weight of the body
The weight of the body can be calculated using the formula:
\[ F_g = mg \]
Where:
- \( m = 0.25 \, \text{kg} \) (mass of the body)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

Substituting the values:
\[ F_g = 0.25 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 2.45 \, \text{N} \]

### Step 3: Apply Newton's second law of motion
According to Newton's second law, the net force acting on the body is equal to the mass of the body multiplied by its acceleration:
\[ F_{\text{net}} = ma \]
Where:
- \( a = 9.2 \, \text{m/s}^2 \) (downward acceleration)

Substituting the values:
\[ F_{\text{net}} = 0.25 \, \text{kg} \times 9.2 \, \text{m/s}^2 = 2.3 \, \text{N} \]

### Step 4: Relate the forces
The net force can also be expressed as the difference between the gravitational force and the frictional force:
\[ F_{\text{net}} = F_g - F_f \]
Substituting the known values:
\[ 2.3 \, \text{N} = 2.45 \, \text{N} - F_f \]

### Step 5: Solve for the frictional force
Rearranging the equation to solve for \( F_f \):
\[ F_f = 2.45 \, \text{N} - 2.3 \, \text{N} = 0.15 \, \text{N} \]

### Conclusion
The frictional force of the air on the body is \( 0.15 \, \text{N} \).

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