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  • A hollow spherical shell at outer radius floats just submerged under the water surface. The inner radius of the shell is <img alt="r" src="http://entrancecorner.codecogs.com/gif.latex

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 sphecific gravity of the shell material is \frac{27}{8} w.r.t water, the value of r is :
Option: 1 \frac{8}{9}R
Option: 2 \frac{4}{9}R
Option: 3 \frac{2}{3}R
Option: 4 \frac{1}{3}R

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\begin{array}{l} \frac{4}{3} \pi\left(\mathrm{R}^{3}-\mathrm{r}^{3}\right) \rho_{\mathrm{m}} \mathrm{g}=\frac{4}{3} \pi \mathrm{R}^{3} \rho_{\mathrm{w}} \mathrm{g} \\ \\ 1-\left(\frac{\mathrm{r}}{\mathrm{R}}\right)^{3}=\frac{8}{27} \\ \\ \Rightarrow \frac{\mathrm{r}}{\mathrm{R}}=\left(\frac{19}{27}\right)^{1 / 3}=\frac{19^{1 / 3}}{3} \\\\ =0.88 \simeq \frac{8}{9} \end{array}

\Rightarrow r = \frac{8R}{9}

Posted by

Deependra Verma

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