In a cylindrical container open to the atmosphere from the top a liquid is filled upto 10 m depth. Density of the liquid varies with depth from the surface as ρ ( h ) = 100 + 6 h 2 where h is in meter

Question

In a cylindrical container open to the atmosphere from the top a liquid is filled upto 10 m depth. Density of the liquid varies with depth from the surface as ρ ( h ) = 100 + 6 h 2 where h is in meter and ρ is in kg / m 3 . The pressure at the bottom of the container will be : (atmosphere pressure = 1 0 5 Pa , g = 10 m / sec 2 )

TestHub · Accepted Answer

Add atmospheric pressure to the hydrostatic pressure:
$p = p_{0} + g \int_{0}^{10} ρ (h) d h$
$p = 1 0^{5} + 10 \int_{0}^{10} (100 + 6 h^{2}) d h$
$\int_{0}^{10} (100 + 6 h^{2}) d h$
$= [100 h + 2 h^{3}]_{0}^{10} = 3000$
$p = 1 0^{5} + 10 (3000)$
$p = 1.3 \times 1 0^{5} Pa$
Option D.

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