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NEET 2016 (Phase 1) · Archimedes' Principle & Floatation

Archimedes' Principle & Floatation question from NEET 2016 (Phase 1)

Q21NEET 2016 · PHASE 1Medium

Archimedes' Principle & Floatation

Two non-mixing liquids of densities ρ\rho and nρ\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

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Answer: (b)

  1. Length pLpL is in liquid nρn\rho and (1−p)L(1-p)L in liquid ρ\rho.
  2. Weight = upthrust: dALg=nρApLg+ρA(1−p)Lgd A L g = n\rho A pL g + \rho A (1-p) L g
  3. d=ρ [np+1−p]={1+(n−1)p}ρd = \rho\,[np + 1 - p] = \{1 + (n-1)p\}\rho
  4. So the answer is (b).
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