A stone attached to one end of string is revolved around a stick so that the string winds upon the stick and gets shortened. What is conserved ?

Options

A. angular momentum
B. linear momentum
C. kinetic energy
D. none of the above

Answer

To solve the problem, we need to analyze the situation involving the stone attached to a string that is being revolved around a stick. Let's break down the steps to determine what is conserved in this scenario.

### Step-by-Step Solution:

1. **Understand the System**:
- We have a stone attached to one end of a string. The other end of the string is wound around a stick. As the stone revolves, the string gets shorter because it is winding around the stick.

2. **Identify Forces Acting on the Stone**:
- The stone is undergoing circular motion. The only forces acting on it are the tension in the string and the gravitational force. However, since the stick is fixed and there are no external torques acting on the system, we can analyze the motion in terms of angular momentum.

3. **Angular Momentum**:
- Angular momentum (L) for an object in circular motion is given by the formula:
\[ L = mvr \]
where \( m \) is the mass of the stone, \( v \) is its tangential velocity, and \( r \) is the radius of the circular path (length of the string).

4. **Conservation of Angular Momentum**:
- In the absence of external torques, the angular momentum of the system is conserved. As the stone moves in a circle and the string winds up, the radius \( r \) decreases, which means that the velocity \( v \) must increase to keep the product \( mvr \) constant (since \( L \) is conserved).

5. **Conclusion**:
- Therefore, the quantity that is conserved in this scenario is the angular momentum of the stone.

### Final Answer:
**Angular momentum is conserved.**

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