A simple barometer is constructed using a liquid \(Q_{1}\) of density 16.2\(g/cm^{3}\). Calculate the least lenth of the tube to be used to measure pressure of 1.5atm. [Density of mercury = 13.6\(g/cm^{3}\), 1atm = 76.0 cm of Mercury]
A
1358mm
B
957mm
C
760mm
D
638mm
Verified Correct Answer: D.
Physical Principles & Numerical Solution
Let \(h_{Q}\) and \(\rho_{Q}\) be the least length and the density of \(Q_{1}\)
while \(h\) and \(\rho\) are the length and density of mercury respectively.
\(h\times \rho \times g = h_{Q} \times \rho_{Q} \times g\)
\(76cm \times 13.6 \times 10 = h_{Q} \times 16.2 \times 10\)
\(h_{Q} = \frac{76\times13.6\times10}{16.2\times10}\)
\(h_{Q} = \frac{10336}{162}\)
\(h_{Q} \approxeq 63.8cm = 638mm\)
Source: Myschool Past Questions Archive (Record #49762)