Fluid Mechanics Viscosity Question 260
Question: A sphere of solid material of specific gravity 8 has a concentric spherical cavity and just sinks in water. The ratio of radius of cavity to that of outer radius of the sphere must be
Options:
A) $ \frac{{{7}^{1/3}}}{2} $
B) $ \frac{{{5}^{1/3}}}{2} $
C) $ \frac{{{9}^{1/3}}}{2} $
D) $ \frac{{{3}^{1/3}}}{2} $
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Answer:
Correct Answer: A
Solution:
[a] Let $ \rho $ be the density of the material, $ {\rho_{0}} $ be the density of water when the sphere has just started sinking, the weight of the sphere = weight of water displaced (approx.) $ \Rightarrow ,,,\frac{4}{3}\pi (R^{3}-r^{3})\rho g=\frac{4}{3}\pi R^{3}{\rho_{0}}g $ $ \Rightarrow ,,(R^{3}-r^{3})\rho =R^{3}{\rho_{0}}\Rightarrow \frac{(R^{3}-r^{3})}{R^{3}}=\frac{{\rho_{0}}}{\rho } $ $ \Rightarrow ,,\frac{r}{R}=\frac{{{(7)}^{1/3}}}{2} $
BETA
