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A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is 27/8 w.r.t. water, the value of r is:
- 4R/9
- 8R/9
- 1/3 R
- 2/3 R
Correct answer: 8R/9
Solution
The specific gravity of the shell material indicates that it is denser than water, and since the shell is floating just submerged, the weight of the water displaced must equal the weight of the shell. By applying the principle of buoyancy and the relationship between the volumes of the inner and outer spheres, we can derive that the inner radius must be 8R/9 to satisfy these conditions.
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