The contact force exerted by a body A on another body B is equal to the normal force between the bodies. We concude that

Options

A. the surface must be frictionless
B. the force of friction between the bodies is zero
C. the magnitude of normal force equals that of friction
D. the bodies may be rough but they don't slip on each other.

Answer

To solve the question, we need to analyze the relationship between the contact force and the normal force between two bodies A and B.

### Step-by-Step Solution:

1. **Understanding the Forces**:
The contact force exerted by body A on body B is defined as the force that acts at the interface of the two bodies. The normal force (Fn) is the perpendicular force exerted by a surface to support the weight of an object resting on it.

2. **Given Condition**:
We are given that the contact force (Fc) is equal to the normal force (Fn) between the bodies:
\[ Fc = Fn \]

3. **Analyzing the Forces**:
The contact force can also be expressed in terms of the frictional force (F) and the normal force (Fn) using the Pythagorean theorem:
\[ Fc = \sqrt{F^2 + Fn^2} \]

4. **Substituting the Condition**:
Since we know that \(Fc = Fn\), we can substitute this into the equation:
\[ Fn = \sqrt{F^2 + Fn^2} \]

5. **Squaring Both Sides**:
To eliminate the square root, we square both sides:
\[ Fn^2 = F^2 + Fn^2 \]

6. **Simplifying the Equation**:
By subtracting \(Fn^2\) from both sides, we get:
\[ 0 = F^2 \]

7. **Conclusion About Friction**:
Since \(F^2 = 0\), we conclude that the frictional force (F) is zero:
\[ F = 0 \]

8. **Interpreting the Results**:
The conclusion that the frictional force is zero implies that:
- The surfaces may not necessarily be frictionless (option 1 is not necessarily true).
- The force of friction between the bodies is indeed zero (option 2 is correct).
- The magnitude of normal force does not equal the friction force since the friction force is zero (option 3 is false).
- The bodies may be rough but do not slip on each other, indicating no relative motion (option 4 is true).

### Final Answer:
The correct conclusions are:
- Option 2: The force of friction between the bodies is zero.
- Option 4: Bodies may be rough, but they do not slip on each other.