# Comparison of densities of liquids using Hare’s apparatus

Liquids of different densities are placed in glass pots as shown above.
When the gas tap is opened each liquid rises to different height h1 and h2.Since they are subjected to the same gas supply,
-Measure the height of the liquids in the two arms, h1 and h2.

PA=PA

H+h1ρ1g=H+h1ρ1g

h1ρ1=h1ρ1

Example 1
Water and kerosene are placed in U-tube containing mercury as shown above. Determine the density of kerosene?

Pressure of kerosene= Pressure of water (since both tube are open to the atmosphere)

PA=PA

H+h1ρ1g=H+h1ρ1g

h1ρ1=h1ρ1 8(1000)=10ρ1

ρ1=800 kgm−3

Example 2
The diagram below shows heights to which liquids A and B have risen in an inverted U-tube, when some air has been pumped at P. Find the density of liquid B if that of A is 800 kgm−3.[Ans: 𝜌=640 kgm−3]

Example 3
The atmospheric pressure at the bottom of a mountain is 100000Pa. If the mountain is 800m high, and the density of air is1.25 kgm−3. Find the pressure at the top of the mountain.

Solution:

𝐏𝐛𝐨𝐭𝐭𝐨𝐦=𝐏𝐭𝐨𝐩+𝐡𝛒𝐠

100000=Ptop+800(1.25)(10)

Ptop=90000 Pa