Question

A hollow sphere of inner and outer diameters of 12 cm and 16 cm respectively floats half submerged in water. The specific gravity of the material of the sphere in CGS units is:

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

Answer 1

The correct option is C 0.865

For equilibrium, the weight of sphere must balance buoyancy force.

Volume$=\frac{4}{3}\pi [8^3\times {10}^{-6}-6^3\times {10}^{-6}]=\frac{4}{3}\pi 296\times {10}^{-6}{F}_b=F_w\frac{1}{2}\times \frac{4}{3}\pi \times 512\times {10}^{-6}\times {\rho }_{air}g=\frac{4}{3}\pi \times 296\times {10}^{-6}\times {\rho }_{material}g\frac{{\rho }_{material}}{{\rho }_{air}}=\frac{512}{2\times 296}=0.865$