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The centre of mass of a solid cone along...

The centre of mass of a solid cone along the line form the center of the base to the vertex is at

A

One-fourth of the height

B

One-third of the height

C

One-fifth of the height

D

None of these

Text Solution

AI Generated Solution

The correct Answer is:
To find the center of mass of a solid cone along the line from the center of the base to the vertex, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Geometry of the Cone**: - Consider a solid cone with height \( H \) and a circular base. The vertex of the cone is at the top, and the center of the base is at the bottom. 2. **Understand the Center of Mass Concept**: - The center of mass of an object is the point where the mass of the object can be considered to be concentrated. For symmetrical objects, it often lies along the axis of symmetry. 3. **Determine the Position of the Center of Mass**: - For a solid cone, the center of mass is located along the vertical axis from the base to the vertex. 4. **Use the Formula for the Center of Mass of a Solid Cone**: - The center of mass of a solid cone is located at a distance of \( \frac{H}{4} \) from the base of the cone. This is derived from the integration of the mass distribution within the cone. 5. **Conclusion**: - Therefore, the center of mass of the solid cone along the line from the center of the base to the vertex is at a height of \( \frac{H}{4} \) from the base. ### Final Answer: The center of mass of a solid cone along the line from the center of the base to the vertex is at a distance of \( \frac{H}{4} \) from the base. ---
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