A hollow metal sphere is found to float in water with the highest point just touching the free surface of water. If `d` is the density of the metal in cgs units, the fraction that represents the volume of the hollow in terms of the volume of the sphere is

Options

A. `(1)/(d)`
B. `(1-(1)/(d))`
C. `(d)/((d-1))`
D. `(1+(1)/(d))`

Answer

B

Explanation

`(V_("cavity"))/(V_(S))=(V_(S)-V_("metal"))/(V_(S))=1-(V_("metal"))/(V_(S))=1-(d_(W))/(d)`