Question

A solid sphere of radius R has a concentric cavity of radius R/2 inside it. The sphere is found to just float in water with the highest point of it touching the water surface. The specific gravity of the material of the sphere is:

• A. $1$
• B. $7/8$
• C. $8/7$
• D. $8/9$

Answer 1

The correct option is C $8/7$

Upward trust of the water to the solid sphere$=\frac{4}{3}\pi R^3\times 1\times g$
Now, for equilibrium, upward trust = weight of the solid
$=\frac{4}{3}\pi (R^3-\frac{R^3}{8})d\times g=\frac{4}{3}\pi R^{3}g$

$d_{solid}=\frac{1}{(1-\frac{1}{8})}=\frac{8}{7}$
$\therefore specificgravityofthematerial=\frac{d_{solid}}{d_{vater}}=\frac{8}{7}$