Two bodies having the same mass 5kg each have different surface areas `20m^2` and `10m^(2)` in contact with a horizontal plane. If the coefficient of friction is 0.4, the forces of friction that come into play when they are in motion will be in the ratio

Options

A. `1:1`
B. `1:2`
C. `2:1`
D. `1:4`

Answer

To solve the problem, we need to determine the forces of friction acting on two bodies with the same mass but different surface areas when they are in motion. The coefficient of friction is given as 0.4.

### Step-by-step Solution:

1. **Identify the Mass of Each Body**:
Each body has a mass \( m = 5 \, \text{kg} \).

2. **Identify the Coefficient of Friction**:
The coefficient of friction \( \mu = 0.4 \).

3. **Calculate the Normal Force**:
The normal force \( N \) acting on each body is equal to its weight, which can be calculated using the formula:
\[ N = m \cdot g \]
where \( g \) (acceleration due to gravity) is approximately \( 9.8 \, \text{m/s}^2 \).
\[ N = 5 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 49 \, \text{N} \]

4. **Calculate the Force of Friction**:
The force of friction \( F_f \) can be calculated using the formula:
\[ F_f = \mu \cdot N \]
Substituting the values we have:
\[ F_f = 0.4 \cdot 49 \, \text{N} = 19.6 \, \text{N} \]

5. **Determine the Ratio of Forces of Friction**:
Since both bodies have the same mass and the same coefficient of friction, the force of friction acting on both bodies will be the same. Therefore, the ratio of the forces of friction for the two bodies is:
\[ \text{Ratio} = \frac{F_{f1}}{F_{f2}} = \frac{19.6 \, \text{N}}{19.6 \, \text{N}} = 1 \]

### Conclusion:
The forces of friction that come into play when the two bodies are in motion will be in the ratio of \( 1:1 \).