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_0` is more than 0.5
D. Less than half-filled if ` rho_c ` is less than 0.5

Answer

A

Explanation

Let `V_(w)` = volume of water in shell
`V_(a)` = volume of air in shell, `V_(m)` = volume of material of shell
then, `V_(w)rho_(w)g+V_(m)(Srho_(w))g=(V_(w)+V_(a)+V_(m))/(2)rho_(w)g` where S is relative density
`rArrV_(w)=V_(m)(1-2S)+V_(a),"if"" "Sgt(1)/(2)rArrV_(w)ltV_(a),"If"Slt(1)/(2)rArrV_(w)gtV_(a)`