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Question

The dimensions of a wooden raft (density =150 kg/m3) are 3.0 m×3.0 m×1.0 m. What maximum load can it carry in seawater so that the plank just floats in water (density=1020 kg/m3)?

A
1350 kg
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B
7830 kg
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C
9200 kg
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D
19,500 kg
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Solution

The correct option is D 7830 kg
Buoyancy is the upward force that an object feels from the water and when compared to the weight of the object.

Buoyancy force can be calculated with the equation
Fb=Vs×D×g

where Fb is the buoyancy force, Vs is the submerged volume, D is the density of the fluid the object is submerged in, and g is the force of gravity.

It can also be given as the sum of the weight of the raft and the weight of the load. That is, Wraft+Wload = Fb=Vs×D×g.

The weight of the raft
Wraft=VraftDraftg.

At maximum load, Volume of water displaced is equal to volume of the raft.

max(Wload)=(DwaterDraft)Vraftg.
=(1020kg/m3150kg/m3)(3m×3m×1m)g
=7830kg.

Hence, the maximum load the raft can carry sea water so that the plank just floats in water is 7830kg.

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