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 one by one.

### Step-by-Step Solution:

1. **Analyze the Pencil:**
- A pencil is a solid cylindrical object.
- The center of mass of a solid object lies within its volume.
- **Conclusion:** The center of mass of a pencil lies inside the body.

2. **Analyze the Shot Put:**
- A shot put is a solid sphere.
- Similar to the pencil, the center of mass of a solid sphere is located at its geometric center, which is inside the sphere.
- **Conclusion:** The center of mass of a shot put lies inside the body.

3. **Analyze the Dice:**
- A dice is a solid cube.
- The center of mass of a solid cube is also at its geometric center, which is located inside the cube.
- **Conclusion:** The center of mass of a dice lies inside the body.

4. **Analyze the Bangle:**
- A bangle is typically in the shape of a hollow ring.
- For hollow objects like rings, the center of mass is located at the center of the ring, which is outside the material of the ring itself.
- **Conclusion:** The center of mass of a bangle lies outside the body.

### Final Answer:
The object for which the center of mass lies outside the body is the **bangle**.