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A hydrometer stem has a length 30 cm. If...

A hydrometer stem has a length 30 cm. If the hydrometer is immersed in water , its floatation bulb just sinks. If the same hydrometer is immersed in a liquid having density of `500 kg m^(-3)`, two-third of the stem is immersed. Find the least specific gravity of a liquid that can be measured using the hydrometer.

Text Solution

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Let 'V' be volume of the hydrometer upto the beginning of its stem (i.e., volume of gravity bulb + floatation bulb)
Let 'a' be the area of cross section of the stem. When the hydrometer is immersed in water, `Vxx1` = mass of hydrometer.
Density of the given liquid = 500 kg `m^(-3)=0.5" g cm"^(-3)`
Length of the stem immersed in the liquid
`=(2)/(3)` (totat length) `=(2)/(3)xx30=20cm`
`:.` volume of the hydrometer in the liquid = V+20a
`:.` mass of liquid displaced= (V+20a)0.5
= mass of hydrometer
`:.(V+20a)0.5=V`
`rArrV+20a=2Vora=(V)/(20)`
Let 'p' be density of the liquid on which the hydrometer floats upto its full length of stem, then mass of hydrometer =(V+30a)p=V
`rArrp=(V)/(V+30((V)/(20)))rArrp=0.4`
`:.` least specific gravity of the liquid that can be measured using the hydrometer is 0.4.
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