Question

A sphere of solid material of relative density $9$ has a concentric spherical cavity and just sinks in water. If the radius of sphere be $R$, then the radius of 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. $r^3 = {\sqrt \frac{2}{3}} R^3$

Answer 1

Answer: (A)

Weight of the sphere = Weight of water displaced
$\left(\frac{4}{3} \pi R^{3}-\frac{4}{3} \pi r^{3}\right) g \times g=\frac{4}{3} \pi R^{3} \times 1 \times g $
$\Rightarrow 9 R^{3}-R^{3}=9 r^{3} $
$\Rightarrow 9 r^{3}=8 R^{3} $
$r^{3}=\left(\frac{8}{9}\right) R^{3}$