Question

A hollow spherical body of inner and outer radii 6 cm and 8 cm respectively floats half-submerged in water. Find the density of the material of the sphere.

Answer 1

$r_2$ = 8 cm, $r_1$ = 6 cm

Here, $m^2$ =Upward thrust

$\Rightarrow V_{pg}=\left(\frac{V}{2}\right)\left(\rho w\right)\times g$

[where ${\rho }_w$ = density of water]

$\Rightarrow =\left(\frac{4}{3}\pi r_1^3\right)\rho =\left(\frac{1}{2}\right)\frac{4}{3}\pi r_2^3\times {\rho }_w$

$\Rightarrow (r_2^3-r_1^3)\times \rho =\left(\frac{1}{2}\right)r_2^3\times 1$

$\Rightarrow (8{)}^3-(6{)}^3\times \rho =\left(\frac{1}{2}\right)(8{)}^3\times 1$

$\Rightarrow \rho =\frac{512}{2\times (512-216)}$

= $\frac{512}{2\times 296}$

= 0.865 gm/cc = 865 $kg/m^3$