A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If `rho_c` is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

Options

A. more than half-filled if `rho_(c)` is less than 0.5
B. more than half-filled if `rho_(c)` is more than `1.0`
C. half-filled if `rho_(c)` is more than 0.5
D. less than half-filled if `rho_(c)` is less than 0.5

Answer

A

Explanation

`(V_(m)+V_(a)+V_(w))/(2)rho_(w)g=V_(m)rho_(c)rho_(w)g+V_(w)rho_(w)g`
`V_(w)=V_(m)(1-2rho_(c))+V_(a)` if `rho_(c) gt (1)/(2) implies V_(w) lt V_(a)`
if `rho_(c) lt (1)/(2) rArr V_(w) lt V_(a)`
Where `V_(w)=` volume occupied by water in the shell
`V_(a)=` volume occupied by air in the shell
`V_(m)=` volume of the material in the shell