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Question

The density of liquid in which hydrometer sinks to the bottom of stem is X gcm−3 . Find [X]. {Where , [] is a step function}

A
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B
1
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C
2
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D
9
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Solution

The correct option is B 1
Let the volume of hydrometer bulb be V.
When hydrometer sinks to the mark 5 cm of the stem.
Using the law of flotation, we have
(V+5)×Dw×g=200×g
Because, Dw=1g/cm3.
V=195cm3.
When the hydrometer sinks to the bottom,
195×DL×g=200×g.
DL=200195=1.0g/cm3.
Hence, the density of liquid in which hydrometer sinks to the top of stem is 1g/cm3 =X .

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