Physics And Measurement Question 151
Question: Frequency is the function of density $ (\rho ) $ , length $ (a) $ and surface tension $ (T) $ . Then its value is?
[BHU 2003]
Options:
A) $ k{{\rho }^{1/2}}{{a}^{3/2}}\mathbf{/}\sqrt{T} $
B) $ k{{\rho }^{3/2}}{{a}^{3/2}}/\sqrt{T} $
C) $ k{{\rho }^{1/2}}{{a}^{3/2}}/{{T}^{3/4}} $
D) $ k{{\rho }^{1/2}}{{a}^{1/2}}/{{T}^{3/2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ n=k{{\rho }^{a}}a^{b}T^{c} $
where $ [\rho ]=[M{{L}^{-3}}],\ [a]=[L] $
and $ [T]=[M{{T}^{-2}}] $
Comparing both sides, we get $ a=\frac{1}{2},b=\frac{3}{2} $
and $ c=\frac{-1}{2} $
$ \eta =\frac{k{{\rho }^{1/2}}{{a}^{3/2}}}{\sqrt{T}} $
