When a stone is projected which remains constant?

Options

A. Angular momentum
B. Linear momentum
C. Vertical component of velocity
D. Horizontal component of velocity

Explanation

To determine which quantity remains constant when a stone is projected, we can analyze the motion of the stone in terms of its components. Here's a step-by-step solution:

### Step 1: Understand the Components of Motion
When a stone is projected, it follows a projectile motion path. This motion can be broken down into horizontal and vertical components. The initial velocity \( u \) can be resolved into:
- Horizontal component: \( V_x = u \cos(\theta) \)
- Vertical component: \( V_y = u \sin(\theta) \)

### Step 2: Analyze the Forces Acting on the Stone
In projectile motion, the only force acting on the stone after it is projected is the gravitational force, which acts downward with a magnitude of \( mg \). This force affects the vertical motion but not the horizontal motion.

### Step 3: Determine the Effect of Gravity on the Components
- **Vertical Component (V_y)**: The vertical component of velocity \( V_y \) changes due to the gravitational force. It decreases as the stone rises and increases as the stone falls. Therefore, \( V_y \) is not constant.
- **Horizontal Component (V_x)**: The horizontal component of velocity \( V_x \) remains constant because there are no horizontal forces acting on the stone (assuming air resistance is negligible). Thus, \( V_x \) is constant.

### Step 4: Analyze Momentum
- **Linear Momentum (p)**: The linear momentum \( p \) of the stone is given by \( p = mV \), where \( V \) is the resultant velocity. Since \( V_y \) is changing, the total linear momentum \( p \) is also changing.
- **Angular Momentum (L)**: Angular momentum depends on the linear momentum and the position vector. Since linear momentum is not constant, angular momentum will also not be constant.

### Conclusion
From the analysis, we can conclude that the only quantity that remains constant when a stone is projected is the horizontal component of velocity \( V_x \).

Thus, the correct answer is:
**The horizontal component of velocity remains constant.**

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