A hollow spherical body of inner and outer radii $6 c m$ and $8 c m$ respectively, floats half submerged in water. The density of the material of the sphere is

865 k g / m^{3}

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600 k g / m^{3}

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700 k g / m^{3}

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665 k g / m^{3}

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Solution

The correct option is A $865 k g / m^{3}$
As the hollow body is floating,
downward force=upward force
upward force $= \frac{2}{3} π {(8)}^{3} g$ .........(1)
Downwards force $= \frac{4 π}{3} (8^{3} - 6^{3}) σ g$ .........(2)
Now,

from equation 1 and 2 we get,
$= \frac{8^{3}}{2 (8^{3} - 6^{3})} = σ$
$σ = 0.86486 g / c m^{3}$
$σ = 865 k g / m^{3}$

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