The centre of gravity of a thin hollow cone lies on the axis of symmetry at a height of:
Try it first: pick an option, then read the explanation.
Correct answer: B. one-third of the total height above the base
Asked in SSC JE 04/03/2017 (Morning)
Detailed Explanation
A thin hollow cone is just its curved surface. Unrolled, it is made of thin triangular strips from the base circle to the apex, each with its centroid at one-third of the height from the base.
Why “one-third of the total height above the base” Is Correct
Since every strip has its centroid at h/3 above the base, the whole surface does too: one-third of the height above the base. A solid cone has more volume near the base, which lowers its centroid to h/4.
| Body | Centroid above the base |
|---|---|
| Thin hollow cone (curved surface) | h/3 |
| Solid cone | h/4 |
| Solid hemisphere | 3r/8 |
| Thin hollow hemisphere | r/2 |
| Triangle (plane area) | h/3 |
Why the Other Options Are Wrong
- A. one-half of the total height above the base: h/2 is the centroid of a cylinder, not a cone.
- C. one-fourth of the total height above the base: h/4 is the centroid of a solid cone.
- D. none of these: h/3 is listed, so (d) is wrong.
Key Point
Hollow cone: h/3; solid cone: h/4 above the base.
Key Concepts for Students
- Plane triangle: centroid h/3 from the base.
- Pappus's theorems link centroids to surface areas and volumes.
- Hemisphere: solid 3r/8, hollow r/2 from the flat face.
Practice more: this is question 26 in Bending and Shear Stress MCQs – Part 2. Try the whole set and check every answer instantly.