Physics And Measurement Question 216
Question: In order to measure physical quantities in the sub-atomic world, the quantum theory often employs energy [E], angular momentum [J] and velocity [c] as fundamental dimensions instead of the usual mass, length and time. Then, the dimension of pressure in this theory is
Options:
A) $ \frac{{{[E]}^{4}}}{{{[J]}^{3}}{{[c]}^{3}}} $
B) $ \frac{{{[E]}^{2}}}{[J][c]} $
C) $ \frac{[E]}{{{[J]}^{2}}{{[c]}^{2}}} $
D) $ \frac{{{[E]}^{3}}}{{{[J]}^{2}}{{[c]}^{2}}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ [E]=[ML^{2}{{T}^{-2}}]………(i) $
$ [J]=[ML^{2}{{T}^{-1}}] $ ….. (ii)
$ [C]=[L{{T}^{-1}}] $ ….. (iii)
Solving (i), (ii) and (iii) we get, $ [ \frac{E}{C^{2}} ]=[M],[ \frac{JC}{E} ]=[L]and[ \frac{J}{E} ]=[T] $ Now, [Pressure] = $ [M{{L}^{-1}}{{T}^{-2}}] $
$ =[ \frac{E}{C^{2}} ]\times [ \frac{E}{JC} ]\times [ \frac{E^{2}}{J^{2}} ]=\frac{{{[E]}^{2}}}{]J^{3}][C^{3}]} $
