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Topic: Fluid pressure, Pascal's law and applications· Properties of Solids and Liquids

Two non-mixing liquids of densities ρ and nρ (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p < 1) in the…

Two non-mixing liquids of densities \(\rho\) and \(n\rho\) (n > 1) are put in a container. The height of each liquid is h. A solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length \(pL\) (p < 1) in the denser liquid. The density d is equal to :

1. \(\{1+(n+1)p\}\rho\)

2. \(\{2+(n+1)p\}\rho\)

3. \(\{2+(n-1)p\}\rho\)

4. \(\{1+(n-1)p\}\rho\)

1 answer

Best answer

Answer: 4. \(\{1+(n-1)p\}\rho\)

Key idea: weight of cylinder equals total buoyant force.

  1. Length \(pL\) is in the denser liquid (\(n\rho\)); remaining \((1-p)L\) is in the lighter liquid (\(\rho\)).
  2. \(d\,LAg=pLA\,n\rho g+(1-p)LA\rho g\).
  3. \(d=\rho[np+1-p]=\{1+(n-1)p\}\rho\).
Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report
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