Physics And Measurement Question 131
Question: A physcial quantity $ x $ depends on quantities $ y $ and $ z $ as follows: $ x=Ay+B\tan Cz $ , where $ A,B $ and $ C $ are constants. Which of the following do not have the same dimensions
[AMU (Engg.) 2001]
Options:
A) $ x $ and $ B $
B) $ C $ and $ {{z}^{-1}} $
C) $ y $ and $ B/A $
D) $ x $ and $ A $
Show Answer
Answer:
Correct Answer: D
Solution:
$ x=Ay+B\tan Cz $
From the dimensional homogenity
$ [x]=[Ay]=[B]\Rightarrow [ \frac{x}{A} ]=[y]=[ \frac{B}{A} ] $
$ [Cz]=[M^{0}L^{0}T^{0}]= $ Dimension less $ x $ and $ B $ ; $ C $
and $ {{Z}^{-1}};y $
and $ \frac{B}{A} $
have the same dimension but $ x $ and $ A $ have the different dimensions.
