Two non-mixing liquids of densities ρ and n ρ n > 1 are put in a container. The height of each liquid is…

1. $\left\{1+\left(\mathrm{n}+1\right)\mathrm{p}\right\}\mathrm{\rho }$
2. $\left\{2+\left(\mathrm{n}+1\right)\mathrm{p}\right\}\mathrm{\rho }$
3. $\left\{2+\left(\mathrm{n}-1\right)\mathrm{p}\right\}\mathrm{\rho }$
4. $\left\{1+\left(\mathrm{n}-1\right)\mathrm{p}\right\}\mathrm{\rho }$

Solution

${\mathrm{f}}_0=\mathrm{m}\mathrm{g}$
$\mathrm{\rho }\mathrm{A}\left(1-\mathrm{p}\right)\mathrm{L}\mathrm{g}+\mathrm{n}\mathrm{\rho }\mathrm{A}\mathrm{p}\mathrm{L}\mathrm{g}=\mathrm{d}\mathrm{A}\mathrm{L}\mathrm{g}$
$\mathrm{\rho }\left(1-\mathrm{p}\right)+\mathrm{n}\mathrm{\rho }\mathrm{p}=\mathrm{d}$
$\left[1-\mathrm{p}+\mathrm{n}\mathrm{p}\right]\mathrm{\rho }=\mathrm{d}$
$\left[1+\left(\mathrm{n}-1\right)\mathrm{p}\right]\mathrm{\rho }=\mathrm{d}$ .

Asked in: NEET 2016 (Phase 1)

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