Physics 9702 · AS & A Level · Density and pressure

Density and pressure — practice question

A sphere is in equilibrium, floating on the surface of sea water with density $1050\,\text{kg m}^{-3}$, as illustrated in Fig. 2.1.
(a)[2]

$21\%$ of the sphere’s volume lies below the water surface. Calculate the density of the sphere from this information.

(b(i))[3]

The sphere is held so that its whole volume is beneath the water surface, and then released. Calculate the sphere’s initial acceleration.

(b(ii))[3]

The sphere moves upwards with acceleration but is still completely below the water surface. State and explain what happens to the sphere’s acceleration as its velocity starts to increase.

(ii)[3]

As its velocity starts to rise, the sphere still accelerates upwards but remains entirely beneath the water surface. State and explain what happens to its acceleration.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply $W = \rho g V$ or alternatively $F = 1050 \times 9.81 \times 0.21$

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