A person is standing on a rotating table with metal spheres in his hands. If he withdraws his hands to his chest, then the effect on his angular velocity will be. a) increase b) decrease c) remain same d) can't say

Options

A. increase
B. decrease
C. remain same
D. can't say

Explanation

To solve the problem, we need to analyze the situation using the principles of rotational motion, specifically the conservation of angular momentum.

### Step-by-Step Solution:

1. **Understanding the System**:
- A person is standing on a rotating table and is holding metal spheres in his hands.
- When the person pulls his hands in towards his chest, the distribution of mass changes.

2. **Moment of Inertia**:
- The moment of inertia (I) is a measure of how difficult it is to change the rotational motion of an object. It depends on the mass distribution relative to the axis of rotation.
- When the person pulls the spheres closer to his body, the distance of the spheres from the axis of rotation decreases. Therefore, the moment of inertia of the system decreases.

3. **Conservation of Angular Momentum**:
- Angular momentum (L) is conserved in a closed system with no external torques acting on it. The angular momentum is given by the formula:
\[ L = I \cdot \omega \]
where \( \omega \) is the angular velocity.
- Since there are no external torques acting on the system, the initial angular momentum must equal the final angular momentum:
\[ L_{initial} = L_{final} \implies I_{initial} \cdot \omega_{initial} = I_{final} \cdot \omega_{final} \]

4. **Effect of Decreasing Moment of Inertia**:
- As the person pulls the spheres closer, \( I_{final} < I_{initial} \). To conserve angular momentum, if the moment of inertia decreases, the angular velocity must increase to keep the product \( I \cdot \omega \) constant.
- Thus, we can conclude that:
\[ \omega_{final} > \omega_{initial} \]

5. **Final Conclusion**:
- Therefore, the angular velocity of the person on the rotating table will increase when he withdraws his hands to his chest.

### Answer:
The correct option is **a) increase**.

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