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Question

Frequency is the function of density (ρ), length (a) and surface tension (T). Then its value is (k is a constant)

A
kρ1/2a3/2T1/2
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B
kρ1/2a3/2T1/2
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C
kρ1/2a3/2T1/2
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D
kρ1/2a3/2T1/2
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Solution

The correct option is A kρ1/2a3/2T1/2
Frequency (n)=kρaabTc,k= constant
Where density (ρ)=Massvolume
=[M][L3]=[M1L3]
a= length =[L1]
Surface Tension (T)=Forcelength
=M1L1T2L1=[M1T2]
Frequency =1time=[T1]
Now from equation (1)
[T1]=[M1L3]a[L1]b[M1T2]c
[M0L0T1]=[Ma+cL3a+bT2c]
Comparing the powers of LHS and RHS
0=a+cc=a ... (1)
3a+b=0 ... (2)
2c=1c=12 ... (3)
From equation (1) and (3)
a=12
Now from equation (2)
3(12)+b=0
b=32
b=32
Now substituting the value of a,b and c in equation (1)
n=kρ1/2a3/2T1/2

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