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Question: A raft of wood of density \(8\times {{10}^{3}}\text{ Kg }{{\text{m}}^{-3}}\) and mass 120 Kg floats ...

A raft of wood of density 8×103 Kg m−38\times {{10}^{3}}\text{ Kg }{{\text{m}}^{-3}} and mass 120 Kg floats in water. How much weight should be put on the raft to make it just sink?

Explanation

Solution

Any object floats on water when the density of the object is less than the water or liquid. When an object sinks in water it is because the water displaced by the object was less than the weight of the object and this is the reason why object with more surface area floats easily while the object which have very narrow surface sinks immediately

Complete answer:
In this question, we have been told that a wooden raft floats on water and we need to find how much weight we need to put on the raft so that it will sink in water.
Here in this question, we are given with two quantities
Density of wooden raft (d) = 8×103 Kg m−38\times {{10}^{3}}\text{ Kg }{{\text{m}}^{-3}}
Mass of the wooden block (m) = 120 Kg
The volume of the raft can be defined as
Volume=massdensityVolume=\dfrac{mass}{density}
Putting the values, we get
V=120 Kg8×103 Kg m−3V=\dfrac{120\text{ Kg}}{8\times {{10}^{3}}\text{ Kg }{{\text{m}}^{-3}}}
V=0.15 m3V=0.15\text{ }{{\text{m}}^{3}}
Let us assume that “w” be the weight in Kg that should be put on the raft to just sink it
Now, we know that to just sink the raft the weight of the raft should be equal to the amount to water displaced by it
The total weight on the raft would be equal to the mass of the raft plus the amount of weight we need to put to just sink it
Total weight of raft = mass + w (weight we need to put)
Therefore, the condition now becomes
W + m = V + dwW\text{ }+\text{ }m\text{ }=\text{ }V\text{ }+\text{ }{{d}_{w}}
Where dw{{d}_{w}} is the density of water.
Putting the values, we get
w+120 Kg=0.15 m3×1000 kgm−3w+120\text{ Kg}=0.15\text{ }{{\text{m}}^{3}}\times 1000\text{ }kg{{m}^{-3}}
On solving this we get,
w=30 Kgw=30\text{ Kg}
Hence, we can conclude that we need to put 30 Kg of weight on the raft to make it just sink.

Note:
Density is a measure of mass per volume. the typical density of an object equals its total mass divided by its total volume. An object made up of a relatively dense material (such as iron) will have less volume than an object of equal mass made up of some less dense substance (such as water).