For which one of the following does the centre of mass lie outside the body?
A ring
Understanding the Centre of Mass
The centre of mass (CM) of a body is a point where the entire mass of the body is considered to be concentrated. This point behaves as if all external forces are applied directly to it, for translational motion. The location of the centre of mass depends on the distribution of mass within the body.
Centre of Mass Location: Inside or Outside?
For most solid, uniform objects, the centre of mass lies within the physical boundaries of the body. However, for certain shapes, especially those that are hollow or have uneven mass distribution, the centre of mass can lie outside the physical material of the body.
Analyzing the Options
Let's examine each option to determine where its centre of mass is located:
- A fountain pen: A fountain pen is a solid object, even though it might have internal ink reservoirs. The mass is distributed throughout its volume. The centre of mass will be located somewhere inside the pen's physical structure.
- A cricket ball: A cricket ball is a solid sphere, usually uniform in density. For a uniform solid sphere, the centre of mass is exactly at its geometric centre, which is well within the ball's physical body.
- A ring: A ring is a circular object with a hole in the middle. The mass is distributed along the circumference of the ring. The centre of mass of a uniform ring is located at its geometric centre, which is the centre of the circle. This point is in the empty space inside the ring, not on the material of the ring itself. Therefore, the centre of mass lies outside the body of the ring.
- A book: A book is a solid object, typically rectangular. The mass is distributed throughout its pages and cover. For a uniform book, the centre of mass will be near the geometric centre, located within the physical boundaries of the book.
Conclusion on Centre of Mass Location
Based on the analysis, the only object among the given options whose centre of mass lies outside its physical body is the ring.
Revision Table: Centre of Mass Examples
| Object | Shape/Structure | Typical Centre of Mass Location | Inside/Outside Body? |
|---|---|---|---|
| Fountain Pen | Solid/Mostly Solid | Inside the physical body | Inside |
| Cricket Ball | Solid Sphere | At geometric center (inside) | Inside |
| Ring | Hollow Circle | At geometric center (empty space) | Outside |
| Book | Solid Cuboid/Rectangle | Inside the physical body | Inside |
Additional Information on Centre of Mass
The concept of the centre of mass is crucial in physics, particularly in mechanics. It simplifies the analysis of complex systems by allowing us to treat the entire body's mass as being concentrated at a single point. This is especially useful for studying translational motion. For rotation, the distribution of mass around the centre of mass, known as the moment of inertia, is also important.
Examples of other objects where the centre of mass might lie outside the physical body include a hollow sphere, a boomerang, or even a system of multiple discrete particles separated in space.
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