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 then `0.5`
B. More than half filled if `rho_c` is less then `1.0`
C. Half filled if `rho_c` is less than `0.5`
D. Less than half filled if `rho_c` is less than `0.5`

Answer

D

Explanation

`V_0` : volume of shell
`m` : mass of shell
`V_omega` : volume of water on the snell
`W = F_B`
`mg + rho_omega V_omega g = rho_omega(V_0)/(2) g`
`V_omega = (V_0)/(2) - (m)/(rho_omega)`
`V_omega lt (V_0)/(2)`.
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