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 developed in the plank material.
D. none of these

Explanation

To solve the problem, we need to analyze the situation described and evaluate the statements provided regarding the uniform plank being pulled. We will break down the analysis step by step.

### Step 1: Understand the Setup
A uniform plank is resting on a smooth horizontal floor, and a horizontal force is applied at one end. This means that the plank will start to accelerate in the direction of the applied force.

**Hint:** Visualize the plank and the force being applied. Consider how the force affects the motion of the plank.

### Step 2: Identify the Forces Acting on the Plank
The forces acting on the plank include:
- The applied force (F) at one end.
- The weight of the plank acting downwards (mg, where m is the mass of the plank).
- The normal force from the ground acting upwards.

**Hint:** Draw a free-body diagram to visualize the forces acting on the plank.

### Step 3: Analyze the Acceleration of the Plank
Since the plank is uniform and resting on a smooth surface, when the force is applied, the entire plank will accelerate in the direction of the force. The acceleration (a) can be calculated using Newton's second law (F = ma).

**Hint:** Remember that the acceleration is uniform across the plank since it is rigid and uniform.

### Step 4: Evaluate the Development of Stress in the Plank
As the force is applied at one end, the plank will experience a stress gradient along its length. The stress will be highest at the end where the force is applied and will decrease towards the other end.

**Hint:** Consider how stress is defined (force per unit area) and how it varies along the length of the plank.

### Step 5: Review the Statements
Now, we need to evaluate each of the statements given in the question to determine which are correct or incorrect based on our analysis.

1. **Statement A:** The plank accelerates in the direction of the applied force.
- **Correct.** The plank will indeed accelerate in the direction of the applied force.

2. **Statement B:** The stress in the plank is uniform along its length.
- **Incorrect.** The stress is not uniform; it varies along the length of the plank.

3. **Statement C:** A stress is developed in the material of the plank due to the applied force.
- **Correct.** Stress is indeed developed as a result of the applied force.

4. **Statement D:** The plank will not move if the force is applied at one end.
- **Incorrect.** The plank will move as long as the force exceeds any frictional forces (which are negligible on a smooth surface).

### Conclusion
Based on the analysis, the statements that are not correct are B and D.

### Final Answer:
The statements that are not correct are:
- Statement B: The stress in the plank is uniform along its length.
- Statement D: The plank will not move if the force is applied at one end.