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1)

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


A) more than half-filled if ρc , is less than 0.5

B) more than half-filled if ρc is more than 1.0

C) half-filled if ρc is more than 0.5

D) less than half-filled if ρc is less than 0.5

Answer:

Option A

Explanation:

Let V1= total material volume of shell

V2= total inside volume of shell and

x = fraction of V2 volume filled with water.

ln floating condition,
Total weight = Upthrust

      V1ρcg+(xV2)(1)g=(V1+V22)(1)g

 or x=0.5+(0.5+ρc)V1V2

from here we can see that 

      x>0.5 if ρc<0.5