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.
