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Properties of Matter question

2016 · Q153
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Properties of Matter question

2016 · Q153

NEETPhysicsProperties of MatterMCQ+4 / −1
Two non-mixing liquids of densities ρ\rhoρ and nρ\rhoρ (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 ρ\rhoρL (ρ\rhoρ < 1) in the denser liquid. The density d is equal to
  1. A
    {2+(n−1)p}ρ\left\{ {2 + \left( {n - 1} \right)p} \right\}\rho{2+(n−1)p}ρ
  2. B
    {1+(n−1)p}ρ\left\{ {1 + \left( {n - 1} \right)p} \right\}\rho{1+(n−1)p}ρ
  3. C
    {1+(n+1)p}ρ\left\{ {1 + \left( {n + 1} \right)p} \right\}\rho{1+(n+1)p}ρ
  4. D
    {2+(n+1)p}ρ\left\{ {2 + \left( {n + 1} \right)p} \right\}\rho{2+(n+1)p}ρ
View written solutionFree

Correct answer: B

According to Archimedes principle,

Weight of the cylinder = (upthrust)1 + (upthrust)2

i.e., ALdg=(1−p)LAρg+(pLA)nρgALdg = \left( {1 - p} \right)LA\rho g + \left( {pLA} \right)n\rho gALdg=(1−p)LAρg+(pLA)nρg

⇒d=(1−p)ρ+pnρ\Rightarrow d = \left( {1 - p} \right)\rho + pn\rho⇒d=(1−p)ρ+pnρ

=ρ−pρ+npρ= \rho - p\rho + np\rho=ρ−pρ+npρ

=ρ+(n+1)pρ= \rho + \left( {n + 1} \right)p\rho=ρ+(n+1)pρ

=p[1+(n−1)p] = p\left[ {1 + (n - 1)p} \right]=p[1+(n−1)p]

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