Pressure in a fluid-mechanical properties of fluids

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Question

A vessel containing liquid of density $ρ$ is accelerated horizontally with acceleration 10m/ s² in a gravity free space. A small sphere of density 2 $ρ$ is released from rest
with respect to the vessel. Find the initial acceleration of the sphere with respect to the vessel:

Moderate

Solution

$\begin{array}{l} F_{net} = F_{pseudo} - F_{Buoyant} = V \times 2 ρ \times 10 - vρ \times 10 = vρ \times 10 \\ a = \frac{F_{net}}{m} = \frac{vρ \times 10}{v \times 2 ρ} = 5 m / s \end{array}$

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