Question

A hydrometer is a device used to measure the density of a liquid. It is a cylindrical tube weighted at one end, so that it floats with the heavier end downward. The tube is contained inside a large "medicine dropper," into which the liquid is drawn using the squeeze bulb (see the drawing). For use with your car, marks are put on the tube so that the level at which it floats indicates whether the liquid is battery acid (more dense) or antifreeze (less dense). The hydrometer has a weight of W = 5.99 × 10-2 N and a cross-sectional area of A = 6.67 × 10-5 m2. How far from the bottom of the tube should the mark be put that denotes (a) battery acid (? = 1280 kg/m3) and (b) antifreeze (? = 1073 kg/m3)?

Answer 1

weight of the hydrometer w = 5.99 x 10^-2 N

cross sectional area A = 6.67 x 10^-5 m²

a) for battery ? = 1280 kg/m3

for this equilibrium condition

force of buoyancy = weight

i.e.,  ?.g.v = w

? . g . A. L = w (since volume v = A x L )

hence L = w / ? . g. A  

= 5.99 x 10^-2 / (1280 x 9.81 x 6.67 x 10^-5)

= 0.0715 m

=7.15 cm

b) for antifreeze ? = 1073 kg/m3

L = w / ? . g. A  

= 5.99 x 10^-2 / (1073 x 9.81 x 6.67 x 10^-5)

= 0.085 m

= 8.5 cm