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Question

A boat floating in a tank of water is carrying passengers. If the passengers drink some of the water surrounding the boat in the tank , how will it affect the water level of the tank?


A

It will go down

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B

It will rise

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C

It will remain unchanged

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D

It will depend on atmospheric pressure

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Solution

The correct option is C

It will remain unchanged


Let us first consider a situation where you have a container floating in water in a tank and you add V2 volume of water from outside (not from the water in the tank)

We know that the tank will submerge a little further. This will increase the level of the water. Right?

by how much? Let us see

Let us assume mass of the container is m kg volume is V m3

Volume submerged initially is V1 m3

Then, mg=ρω V1gm=ρω V1 - - - - - - (i)

After a volume of V2 is added, let us assume, the volume of container now submerged is V3

From Free body diagram,

mg+ρωV2g=ρωV3g

m+ρωV2=ρωV3

ρωV1+ρωV2=ρωV3 (from (i))

V1+V2=V3

Rise in volume of water = V3V1=V2

The level of water will rise by V2 m3

Now if the V2 volume was taken from the tank itself, the rise will be zero.

The level will remain unchanged


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