# The length of stem of a hydrometer is 10cm and the volume of stem is 10 cubic cm. While floating in pure water, it sinks to the 5cm mark. The mass of hydrometer is 200g. What will be the density of liquid in which hydrometer (i) sinks to the top of stem (ii) sinks to the bottom of stem?

1
by samharsh

2015-02-20T13:23:38+05:30

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Length of hydrometer stem = 10cm
volume of hydrometer stem = 10cm³
So base area (A)= 10cm³ / 10cm = 1cm²

When it is put in pure water, It sinks to 5cm mark
mass of hydrometer = 200g
since it is floating, mass of water displaced = mass of hydrometer = 200g
assuming density of water = 1g/cc

volume of hydrometer(upto 5cm mark) = mass of water displaced/density of water                                                               =200/1
= 200 cc

now if it is put in a liquid where
(i) it sinks to the top of the stem,
the mark till which it sinks is 10cm.

volume of liquid displaced = volume of hydrometer(upto 5cm mark) + volume of hydrometer from 5cm mark to 10 cm mark
= 200 cc + (10-5)cm×1cm²
= 205cc
[(10-5) is the height and 1cm² is the base area]

density of liquid = mass of hydrometer / volume of liquid displaced
= 200/205
= 0.9756 g/cc

(ii) it sinks to the bottom of the stem,
the mark till which it sinks is 0cm.

volume of liquid displaced = volume of hydrometer(upto 5cm mark) - volume of hydrometer from 0cm mark to 5 cm mark
= 200 cc - (5-0)cm×1cm²
= 195cc
[(5-0) is the height and 1cm² is the base area]

density of liquid = mass of hydrometer / volume of liquid displaced
= 200/195
= 1.0256 g/cc