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A sphere of radius R and made of material of relative density \mathrm{\sigma} has a concentric cavity of radius r. It just floats when placed in a tank full of water. The value of the ratio \mathrm{R / r} will be

Option: 1

\mathrm{\left(\frac{\sigma}{\sigma-1}\right)^{1 / 3}}


Option: 2

\mathrm{\left(\frac{\sigma-1}{\sigma}\right)^{1 / 3}}


Option: 3

\mathrm{\left(\frac{\sigma+1}{\sigma}\right)^{1 / 3}}


Option: 4

\mathrm{\left(\frac{\sigma-1}{\sigma+1}\right)^{1 / 3}}


Answers (1)

best_answer

\mathrm{\begin{aligned} & \sigma \times \frac{4}{3} \pi\left(R^3-r^3\right) g=1 \times \frac{4}{3} \pi R^3 g \\ & \frac{R}{r}=\left(\frac{\sigma}{\sigma-1}\right)^{1 / 3} \end{aligned}}

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