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
$\left(\frac{4}{3}\pi R^3-\frac{4}{3}\pi r^3\right)g\times g=\frac{4}{3}\pi R^3\times 1\times g$
$\Rightarrow 9R^3-R^3=9r^3$
$\Rightarrow 9r^3=8R^3$
$r^3=\left(\frac{8}{9}\right)R^3$