Question

A hollow sphere of inner diameter and outer diameter of 12 cm and 16 cm respectively floats half submerged in water. The relative density of material of the sphere is

• A. 8.65
• B. 6.85
• C. 0.865
• D. 0.685

Answer 1

The correct option is C 0.865

$r_{in}=6cm$
$r_0=8cm$
Volume of sphere$\Rightarrow \frac{4}{3}\pi (r_0^3-r_{in}^3)$
Weight = upward thrust of the sphere
VDg = V'dg
$\frac{4}{3}\pi \left(\right(8{)}^3-\left(6{)}^3\right)\times D\times g=\frac{1}{2}\times \frac{4}{3}\pi (8{)}^3\times d\times g$
$\because \text{density of water 'd' is 1}$
$(512-216)\times D=\frac{8\times 8\times 8}{2}\times 1$
$296\times D=256$
$D=\frac{256}{296}=0.8648$
$=0.865g/c{m}^3$