OCR MEI
Further Mechanics Minor
2019
June
— Question 2
4 marks
Exam Board
OCR MEI
Module
Further Mechanics Minor (Further Mechanics Minor)
Year
2019
Session
June
Marks
4
Topic
Dimensional Analysis
2
Write down the dimensions of pressure.
The SI unit of pressure is the pascal (Pa). 15 Pa is equivalent to \(Q\) newtons per square centimetre.
Find the value of \(Q\).
Simon thinks the speed, \(v\), of sound in a gas is given by the formula
\(v = k P ^ { x } d ^ { y } V ^ { z }\),
where \(P\) is the pressure of the gas,
\(d\) is the density of the gas,
\(V\) is the volume of the gas,
\(k\) is a dimensionless constant.
Use dimensional analysis to
find the values of \(x\) and \(y\) and
show that \(z = 0\). [0pt]
[4]
At normal atmospheric pressure the density of air at sea level is \(1.29 \mathrm {~kg} \mathrm {~m} ^ { - 3 }\). Under the same conditions the density of helium is \(0.166 \mathrm {~kg} \mathrm {~m} ^ { - 3 }\).
Given that the speed of sound in air under these conditions is \(340 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), use Simon's formula to find the speed of sound in helium under the same conditions.