Find the friction force due to air on a body of mass 1 kg falling with acceleration `8 m//s^(2)` :-

Options

A. 2 N
B. 4 N
C. Zero
D. None

Answer

To find the friction force due to air on a body of mass 1 kg falling with an acceleration of 8 m/s², we can follow these steps:

### Step 1: Identify the forces acting on the body.
The forces acting on the body are:
- The gravitational force (weight) acting downwards, which is given by \( F_g = mg \).
- The frictional force due to air (drag force) acting upwards, which we will denote as \( F_k \).

### Step 2: Write down the equation 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:
\[ F_{\text{net}} = ma \]
The net force can also be expressed as the difference between the gravitational force and the frictional force:
\[ F_{\text{net}} = F_g - F_k \]
Thus, we can write:
\[ mg - F_k = ma \]

### Step 3: Rearrange the equation to find the frictional force.
From the equation above, we can rearrange it to solve for the frictional force \( F_k \):
\[ F_k = mg - ma \]

### Step 4: Substitute the known values.
We know:
- Mass \( m = 1 \) kg
- Acceleration due to gravity \( g = 9.8 \) m/s²
- Acceleration \( a = 8 \) m/s²

Substituting these values into the equation:
\[ F_k = (1 \, \text{kg} \cdot 9.8 \, \text{m/s}^2) - (1 \, \text{kg} \cdot 8 \, \text{m/s}^2) \]
\[ F_k = 9.8 \, \text{N} - 8 \, \text{N} \]
\[ F_k = 1.8 \, \text{N} \]

### Conclusion:
The friction force due to air on the body is \( 1.8 \, \text{N} \).

---