Physics And Measurement Question 124
Question: If the time period $ (T) $ of vibration of a liquid drop depends on surface tension $ (S) $ , radius $ (r) $ of the drop and density $ (\rho ) $ of the liquid, then the expression of $ T $ is
[AMU (Med.) 2000]
Options:
A) $ T=k\sqrt{\rho r^{3}/S} $
B) $ T=k\sqrt{{{\rho }^{1/2}}r^{3}/S} $
C) $ T=k\sqrt{\rho r^{3}/{{S}^{1/2}}} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ T\propto S^{x}r^{y}{{\rho }^{z}} $
by substituting the dimension of $ [T]=[T] $
$ [S]=[M{{T}^{-2}}],[r]=[L],[\rho ]=[M{{L}^{-3}}] $
and by comparing the power of both the sides $ x=-1/2,y=3/2,z=1/2 $
so $ T\propto \sqrt{\rho r^{3}/S}\Rightarrow T=k\sqrt{\frac{\rho r^{3}}{S}} $
