A uniform plank is resting over a smooth horizontal floor and is pulled by applying a horizontal force at its one end. Which of the following statements are not correct?

Options

A. Stress developed in plank material is maximum at the end at which force is applied and decrease linearly to zero at the other end.
B. A uniform tensile stress is developed in the plank material
C. Since plank is pulled at one end only, plank starts to accelerate along direction of the force. Hence, no stress is developed in the plank material
D. None of these

Explanation

To solve the problem, we need to analyze the situation of a uniform plank being pulled at one end while resting on a smooth horizontal floor. We will evaluate the statements provided and determine which ones are incorrect.

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have a uniform plank of mass \( m \) resting on a smooth horizontal floor.
- A horizontal force \( F \) is applied at one end of the plank.

2. **Identify the Forces**:
- The applied force \( F \) causes the plank to accelerate.
- The acceleration \( a \) of the plank can be described by Newton's second law:
\[ F = ma \]

3. **Analyze Stress Distribution**:
- Stress in a material is defined as the force applied per unit area.
- As the force is applied at one end, the stress will not be uniform throughout the length of the plank.

4. **Calculate the Force at a Distance \( x \)**:
- Let \( L \) be the total length of the plank.
- The force \( F' \) at a distance \( x \) from the end where the force is applied can be expressed as:
\[ F' = \frac{m}{L} (L - x) a \]
- This indicates that the force decreases linearly from \( F \) at \( x = 0 \) to \( 0 \) at \( x = L \).

5. **Determine Stress at Different Points**:
- The stress \( \sigma \) at a distance \( x \) can be expressed as:
\[ \sigma = \frac{F'}{A} \]
- Where \( A \) is the cross-sectional area of the plank.
- As \( x \) increases from \( 0 \) to \( L \), the stress is maximum at \( x = 0 \) and decreases to zero at \( x = L \).

6. **Evaluate the Statements**:
- **Statement 1**: "The stress developed in the plank material is maximum at the end where the force is applied and decreases linearly to zero at the other end."
- This statement is **correct**.
- **Statement 2**: "A uniform tensile stress is developed in the plank material."
- This statement is **incorrect** because the stress is not uniform; it varies along the length of the plank.
- **Statement 3**: "Since the plank is pulled at one end only, the plank starts to accelerate along the direction of force; hence no stress is developed in the plank material."
- This statement is also **incorrect**. Stress is indeed developed in the plank due to the applied force, even though it accelerates.

### Conclusion:
The statements that are **not correct** are:
- A uniform tensile stress is developed in the plank material.
- Since the plank is pulled at one end only, no stress is developed in the plank material.