A barometer is faulty . When the true barometer reading are `73` cm and `75` cm of Hg , the faulty barometer reads `69` cm and `70` cm respectively (i) What is the total length of the barometer tube? (ii) What is the reading when the faulty barometer reads `69.5`cm? (iii) What is the faulty barometer reading when the true barometer reads `74`cm?

Answer

`74` cm , `73.94` cm , `69.52`cm

Explanation

Let `h_(1)` = empty space over Hg-column
For constant temperature process `P_(1)V_(1) = P_(2)V_(2) implies 4 xx h_(1) = 5h_(2)`
where `h_(1) - h_(2) = 1 implies h_(2) = 4 ` & `h_(1) = 5`
(i) Total length of tube = `69+5 = 74 cm "or" 70+4= 74cm`
(ii) When faulty barometer reads `69.5cm`.
`P_(1)V_(1) = P_(2)V_(2), 4h_(1) = 4.5h, h=4.44`
`therefore` True reading = `69.5 +4.44= 73.94`
(iii) When the barometer reads `74`cm `P_(1)V_(1) = P_(2)V_(2) implies 4 xx5 = (74-x)^(2) implies x = 69.528` cm