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.



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