A sphere of solid material of relative density 9 has a concentric spherical cavity and floats&

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9-1.Fluid Mechanics

hard

A sphere of solid material of relative density $9$ has a concentric spherical cavity and floats having just sinked in water. If the radius of the sphere be $R$, then the radius of the cavity $(r)$ will be related to $R$ as :-

A

$r^3 = \frac{8}{9} R^3$

B

$r^3 = \frac{2}{3} R^3$

C

$r^3 = \frac{\sqrt 8}{3} R^3$

D

$r^3 = \sqrt { \frac{2}{3}} R^3$

Solution

$\frac{4}{3} \pi\left(\mathrm{R}^{3}-\mathrm{r}^{3}\right) \rho \mathrm{g}=\frac{4}{3} \pi \mathrm{R}^{3} \rho_{\mathrm{w}} \mathrm{g}$

$9\left(R^{3}-r^{3}\right)=R^{3}$

$r^{3}=\frac{8 R^{3}}{9}$

Standard 11

Physics

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