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JEE Advanced 2012Paper 2
Exam
JEE Advanced
Year
2012
Paper
Paper 2
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Advanced 2012 · Paper 2 · Physics · Mechanical Properties of Fluids

A thin uniform cylindrical shell, closed at both ends, is partially...

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 ρc\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

  1. Amore than half-filled if ρc\rho_{c} is less than 0.50.5.
  2. Bmore than half-filled if ρc\rho_{c} is more than 1.0.
  3. Chalf-filled if ρc\rho_{c} is more than 0.50.5.
  4. Dless than half-filled if ρc\rho_{c} is less than 0.50.5.

Correct answer

A. more than half-filled if ρc\rho_{c} is less than 0.50.5.

Step-by-step solution

Let V1=V_{1}= total material volume of cylindrical shell V2=V_{2}= total inside volume of cylindrical shell and y=y= fraction of V2V_{2} volume filled with water. Total weight = Upthrust (Condition of floatation) ∴V1ρcg+(yV2)(1)g=(V1+V22)(1)g\therefore \quad V_{1} \rho_{c} g+\left(y V_{2}\right)(1) g=\left(\frac{V_{1}+V_{2}}{2}\right)(1) g or y=0.5+(0.5−ρc)V1V2y=0.5+\left(0.5-\rho_{c}\right) \frac{V_{1}}{V_{2}} So, if ρc<0.5\rho_{c} < 0.5 then y>0.5y>0.5
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