A hollow spherical shell of outer radius R floats just submerged… | JEE Main 2020 (5 Sep, Shift 1)

Q15JEE Main 2020 · 5 SEP · SHIFT 1Medium

Archimedes' Principle & Floatation

A hollow spherical shell of 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 $\frac{27}{8}$ w.r.t water, the value of r is:

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Answer: (d)

Just submerged: weight of shell = upthrust on full outer volume.
$\dfrac{27}{8}\cdot\dfrac{4}{3}\pi(R^3 - r^3) = \dfrac{4}{3}\pi R^3 \Rightarrow R^3 - r^3 = \dfrac{8}{27}R^3$
$r^3 = \dfrac{19}{27}R^3 \Rightarrow r = (0.704)^{1/3} R \approx 0.89\,R$
$\dfrac{8}{9} = 0.889$ , so the answer is (d) $\dfrac{8}{9}R$ .

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