For which of the following does the centre of mass lie outside the body ?

Options

A. A pencil
B. A shotput
C. A dice
D. A bangle

Explanation

To determine for which of the given objects the center of mass lies outside the body, we will analyze each option step by step.

### Step 1: Analyze the Pencil
- A pencil is a solid object with mass distributed throughout its length. The center of mass of a solid object lies within its volume.
- **Conclusion**: The center of mass of a pencil lies inside the body.

### Step 2: Analyze the Shot Put
- A shot put is a solid spherical object. Similar to the pencil, its mass is uniformly distributed throughout its volume.
- **Conclusion**: The center of mass of a shot put lies inside the body.

### Step 3: Analyze the Dice
- A dice is also a solid cube with mass uniformly distributed throughout its volume.
- **Conclusion**: The center of mass of a dice lies inside the body.

### Step 4: Analyze the Bangle
- A bangle is typically a hollow ring. The mass is concentrated along the circular edge, and there is no mass in the center of the ring.
- **Conclusion**: The center of mass of a bangle lies at the geometric center of the ring, which is outside the body.

### Final Conclusion
- Among the given options, the only object for which the center of mass lies outside the body is the bangle.

**Answer**: The center of mass lies outside the body for the bangle.

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