A solid metal sphere with density metal isplaced under a fluid and released from

Question

A solid metal sphere with density metal isplaced under a fluid and released from rest. The sphere sinksbecause metal > water. Derive an expression for the magnitude of the initial downwardacceleration of the sphere immediately after it is released. Notice that the volume of the sphere is not given, so youranswer should not depend on the volume V.

Hint: Archimedes's Principle says that the size of the buoyantforce on the sphere is equal to the weight of the displacedfluid.

Is pressure, P=pAhg/A, the same as acceleration? Or do I have tofind the forces, F2-F1=pgA(h2-h1).

Explanation / Answer

downward force - upward force = m a . m g    -     buoyantforce = m a . metal V g -   water V g   =  metal Va           now divide everything by V and by metal .      a =   g ( 1   - water / metal) . There you go

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