Physics And Measurement Question 64

Question: Of the following quantities, which one has dimensions different from the remaining three

[AIIMS 1987; CBSE PMT 1993]

Options:

A) Energy per unit volume

B) Force per unit area

C) Product of voltage and charge per unit volume

D) Angular momentum per unit mass

Show Answer

Answer:

Correct Answer: D

Solution:

Energy per unit volume = $ \frac{[ML^{2}{{T}^{-2}}]}{[L^{3}]}=[M{{L}^{-1}}{{T}^{-2}}] $ F

orce per unit area = $ \frac{[ML{{T}^{-2}}]}{[L^{2}]}=[M{{L}^{-1}}{{T}^{-2}}] $

Product of voltage and charge per unit volume $ =\frac{V\times Q}{Volume}=\frac{VIt}{Volume}=\frac{Power\times Time}{Volume} $
$ \Rightarrow $

$ \frac{[ML^{2}{{T}^{-3}}][T]}{[L^{3}]}=[M{{L}^{-1}}{{T}^{-2}}] $

Angular momentum per unit mass = $ \frac{[ML^{2}{{T}^{-1}}]}{[M]}=[L^{2}{{T}^{-1}}] $

So angular momentum per unit mass has different dimension.



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