A rod of mass m is released on smooth horizontal surface making angle `theta` with horizontal. Then which of the following statement is correct ?

Options

A. Acceleration of rod along vertical is less than g
B. Acceleration of centre of mass along horizontal is zero.
C. Angular acceleration of rod is not constant
D. Momentum of the rod along vertical will remain constant

Answer

To solve the problem step by step, we will analyze the situation of the rod released on a smooth horizontal surface making an angle θ with the horizontal. We will evaluate each of the statements provided in the question.

### Step 1: Understanding the Forces Acting on the Rod
When the rod is released, the following forces act on it:
- The weight of the rod (mg) acting vertically downward.
- The normal force (N) acting perpendicular to the surface.

### Step 2: Analyzing the Components of Weight
The weight of the rod can be resolved into two components:
- Vertical component: \( mg \cos(\theta) \)
- Horizontal component: \( mg \sin(\theta) \)

### Step 3: Applying Newton's Second Law
In the vertical direction:
- The normal force (N) balances the vertical component of the weight.
- Therefore, \( N = mg \cos(\theta) \)

In the horizontal direction:
- The horizontal component of the weight \( mg \sin(\theta) \) causes the rod to accelerate horizontally.

### Step 4: Evaluating Each Statement
1. **Acceleration of rod along vertical is less than g**:
- The rod does not accelerate vertically as the normal force balances the vertical component of weight. Thus, the vertical acceleration is zero, which is not less than g. **This statement is incorrect.**

2. **Acceleration of center of mass along horizontal is zero**:
- The horizontal component of the weight causes the rod to accelerate horizontally. Therefore, the acceleration of the center of mass is not zero. **This statement is incorrect.**

3. **Angular acceleration of rod is not constant**:
- The rod is undergoing translational motion, and the angle θ remains constant during this motion. Therefore, the angular acceleration is zero, which is constant. **This statement is incorrect.**

4. **Momentum of the rod along vertical will remain constant**:
- Since there is no net force acting in the vertical direction (the normal force balances the vertical component of weight), the vertical momentum remains constant. **This statement is correct.**

### Conclusion
The only correct statement is that the momentum of the rod along the vertical will remain constant.

### Final Answer
**The correct statement is: Momentum of the rod along vertical will remain constant.**

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