Normal reaction on a body by a floor depends on its

Options

A. Velocity on the floor
B. Mass
C. Acceleration on the floor
D. Dislpacement on the floor

Answer

To determine how the normal reaction on a body by a floor depends on various factors, we can analyze the forces acting on the body. Here’s a step-by-step solution:

### Step 1: Identify the Forces Acting on the Body
When a body of mass \( m \) is resting on a floor, two primary forces act on it:
- The gravitational force (weight) acting downward, which is given by \( mg \), where \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).
- The normal force (\( N \)) exerted by the floor acting upward, perpendicular to the surface.

**Hint:** Consider the forces acting on the object and their directions.

### Step 2: Apply Newton's Second Law
If the body is at rest or moving with constant velocity, the net force acting on it is zero. According to Newton's second law, we can write:
\[ \Sigma F = 0 \]
This implies:
\[ N - mg = 0 \]
Thus, we can conclude that:
\[ N = mg \]

**Hint:** Remember that for an object at rest, the sum of the forces must equal zero.

### Step 3: Analyze the Dependence of Normal Force
From the equation \( N = mg \), we can see that the normal force \( N \) depends directly on the mass \( m \) of the object. Since \( g \) is a constant (approximately \( 9.8 \, \text{m/s}^2 \)), we can conclude that:
\[ N \propto m \]

**Hint:** Identify which variables are constant and which are changing in your equation.

### Step 4: Evaluate Other Factors
Now, let’s evaluate the other options provided in the question:
- **Velocity on the floor:** The normal force does not depend on the velocity of the object if it is at rest or moving uniformly.
- **Acceleration on the floor:** If the object is not accelerating vertically, the normal force will still equal the weight.
- **Displacement on the floor:** The normal force does not depend on the displacement of the object.

Thus, the only factor that the normal reaction depends on is the mass of the object.

**Hint:** Consider how each factor influences the forces acting on the object.

### Conclusion
The normal reaction on a body by a floor depends on its mass. Therefore, the correct answer is that the normal reaction is directly proportional to the mass of the body.

**Final Answer:** The normal reaction on a body by a floor depends on its mass.