JEE Advanced2012PhysicsMechanical Properties of FluidsActual
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 _ 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
- Amore than half-filled if _ c is less than 0.5 .
- Bmore than half-filled if _ c is more than 1.0.
- Chalf-filled if _ c is more than 0.5 .
- Dless than half-filled if _ c is less than 0.5 .
Correct answer
A. more than half-filled if _ c is less than 0.5 .
Step-by-step solution
Let V₁= total material volume of cylindrical shell V₂= total inside volume of cylindrical shell and y= fraction of V₂ volume filled with water. Total weight = Upthrust (Condition of floatation) V₁ _ c g+ (y V₂ )(1) g= ( V₁+V₂ 2 )(1) g or y=0.5+ (0.5- _ c ) V₁ V₂ So, if _ c 0.5