A) \[\frac{{{[E]}^{4}}}{{{[J]}^{3}}{{[c]}^{3}}}\]
B) \[\frac{{{[E]}^{2}}}{[J][c]}\]
C) \[\frac{[E]}{{{[J]}^{2}}{{[c]}^{2}}}\]
D) \[\frac{{{[E]}^{3}}}{{{[J]}^{2}}{{[c]}^{2}}}\]
Correct Answer: A
Solution :
[a] \[[E]=[M{{L}^{2}}{{T}^{-2}}].........(i)\] \[[J]=[M{{L}^{2}}{{T}^{-1}}]\] ..... (ii) \[[C]\,=[L{{T}^{-1}}]\] ..... (iii) Solving (i), (ii) and (iii) we get, \[\left[ \frac{E}{{{C}^{2}}} \right]=[M],\left[ \frac{JC}{E} \right]=[L]\,and\,\left[ \frac{J}{E} \right]=[T]\] Now, [Pressure] = \[[M{{L}^{-1}}{{T}^{-2}}]\] \[=\left[ \frac{E}{{{C}^{2}}} \right]\times \left[ \frac{E}{JC} \right]\times \left[ \frac{{{E}^{2}}}{{{J}^{2}}} \right]=\frac{{{[E]}^{2}}}{]{{J}^{3}}][{{C}^{3}}]}\]
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