Physics 9702 · AS & A Level · Density and pressure

Density and pressure — practice question

A container is filled by a liquid of density $\rho$ to a depth $h$, as illustrated in Fig. 2.1. The base of the container has area $A$.
(a)[3]

Using the definitions of pressure and density, derive the equation $p = \rho g h$, where $p$ represents the pressure exerted by the liquid on the container base and $g$ is the acceleration of free fall.

(b(i)1)[1]

A small solid sphere falls through the liquid at constant velocity. State the names of the three forces acting on the sphere.

(b(i)2)[1]

State a word equation linking the magnitudes of these forces.

(b(ii))[2]

State and explain the energy changes that happen as the sphere falls.

(c(i))[1]

The liquid in the container is liquid L. Liquid M is then added to the container. The two liquids do not mix. The combined depth of the liquids is $0.17\,\text{m}$. Fig. 2.2 shows how the pressure $p$ inside the liquids varies with height $x$ above the base of the container. Use Fig. 2.2 to state the value of atmospheric pressure.

(c(ii))[2]

Use Fig. 2.2 to find the density of liquid M.

((ii))[2]

State and explain the energy changes that happen as the sphere falls.

(c)

The liquid in the container is liquid L. Liquid M is then added to the container. The two liquids do not mix. The combined depth of the liquids is $0.17\,\text{m}$. Fig. $2.2$ shows how the pressure $p$ inside the liquids varies with height $x$ above the base of the container.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: $\rho = m/V$ or $\rho = m/Ah$

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