Asphere of radius $R$ and made of material of relative density $\sigma$ has a concentric cavity of radius $r$. It just floats when placed in a tank full of water. The value of the ratio $R/r$ will be
Asphere of radius $R$ and made of material of relative density $\sigma$ has a concentric cavity of radius $r$. It just floats when placed in a tank full of water. The value of the ratio $R/r$ will be
- A
${\left( {\frac{\sigma }{{\sigma - 1}}} \right)^{1/3}}$
- B
${\left( {\frac{{\sigma - 1}}{\sigma }} \right)^{1/3}}$
- C
${\left( {\frac{{\sigma + 1}}{\sigma }} \right)^{1/3}}$
- D
${\left( {\frac{{\sigma - 1}}{{\sigma + 1}}} \right)^{1/3}}$
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- [AIIMS 2009]