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In the diagram below, four cones are depicted, each with a height of 12 cm. The position of the center of gravity is indicated by dots located at 9 cm, 8 cm, 4 cm, and 3 cm from the apex of each cone. Which of these cones is completely solid?

In the diagram below, four cones are depicted, each with a height of 12 cm. The position of the center of gravity is indicated by dots located at 9 cm, 8 cm, 4 cm, and 3 cm from the apex of each cone. Which of these cones is completely solid? Physics Competency Focused Practice Questions Class 10 Solutions.
  1. 9 cm
  2. 8 cm
  3. 4 cm
  4. 3 cm

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Answer

9 cm

Reason — For a completely solid cone (of uniform density), the center of gravity (CG) lies at a height of one-fourth the height from the base.

Distance from apex = 34\dfrac{3}{4} x Height

Distance from apex=34×Height\text{Distance from apex} = \dfrac{3}{4} \times \text{Height}
So, for a cone of height 12 cm, CG=34×12=9 cm from the apex\text{CG} = \dfrac{3}{4} \times 12 = 9~\text{cm from the apex}
This means that only the cone with CG at 9 cm from the apex behaves like a completely solid cone.

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