Physics 9702 · AS & A Level · Density and pressure

Density and pressure — practice question

A cylinder is supported from the end of a string. In water, the cylinder is at rest with its axis vertical, as illustrated in Fig. 2.1. The cylinder has weight $0.84\,\text{N}$, height $h$ and a circular cross-section of diameter $0.031\,\text{m}$. The density of the water is $1.0 \times 10^{3}\,\text{kg m}^{-3}$. The pressure difference between the upper and lower faces of the cylinder is $520\,\text{Pa}$.
(a(i))[2]

Calculate the height $h$ of the cylinder.

(a(ii))[2]

Show that the upthrust on the cylinder is $0.39\,\text{N}$.

(a(iii))[1]

Calculate the tension $T$ in the string.

(b(i))[2]

Use Fig. 2.2 to find the acceleration of the cylinder at time $t = 2.0\,\text{s}$.

(b(ii))[2]

The top face of the cylinder is $0.32\,\text{m}$ below the water surface at time $t = 0$. Use Fig. 2.2 to determine the depth of the top face below the surface of the water at time $t = 4.0\,\text{s}$.

(c(i))[1]

State the name of the force that acts on the cylinder when it is moving and does not act on the cylinder when it is stationary.

(c(ii))[2]

State and explain the variation, if any, of the acceleration of the cylinder as it falls downwards through the water.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Application of pressure relation $\Delta p = \rho g \Delta h$

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