Verified Solution • 2025–26 Session moderate

QNEET-2016-Ph-1074: NEET 2016 Physics - Class 11 NEET-2016-Ph-1074 Solution: Two non-mixing liquids of densities \( \) and \(n \) (n > 1)…

Two non-mixing liquids of densities ρ\rho and nρn\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 pLpL (p<1p < 1) in the denser liquid. The density d is equal to {2+(n−1)p}ρ\{2+(n-1)p\}\rho {1+(n−1)p}ρ\{1+(n-1)p\}\rho {1+(n+1)p}ρ\{1+(n+1)p\}\rho {2+(n+1)p}ρ\{2+(n+1)p\}\rho

Multiple Choice Options

  • A {2+(n−1)p}ρ\left\{ {2 + \left( {n - 1} \right)p} \right\}\rho { 2 + ( n _ 1 ) p } _
  • B {1+(n−1)p}ρ\left\{ {1 + \left( {n - 1} \right)p} \right\}\rho { 1 + ( n _ 1 ) p } _
  • C {1+(n+1)p}ρ\left\{ {1 + \left( {n + 1} \right)p} \right\}\rho { 1 + ( n + 1 ) p } _
  • D {2+(n+1)p}ρ\left\{ {2 + \left( {n + 1} \right)p} \right\}\rho { 2 + ( n + 1 ) p } _

Step-by-Step Verified Solution

According to Archimedes principle, Weight of the cylinder = (upthrust) 1 + (upthrust) 2 i.e., A L d g = ( 1 _ p ) L A _ g + ( p L A ) n _ g _ d = ( 1 _ p ) _ + p n _ = _ _ p _ + n p _ = _ + ( n + 1 ) p _ = p [ 1 + ( n _ 1 ) p ]

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