Question

.GOOD MORNING
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Q. no. 7
.Give the solution with full explanations ​​

Answer 1

Answer:

Explanation:

In dimensional analysis,

Length is represented as [L]

Mass is represented as [M]

=> Mass per unit length, m = [ML⁻¹]

Time is represented as [T]

=> Frequency = 1/time = [T⁻¹]

Force = mass x acceleration = [M] x [LT⁻²] = [MLT⁻²]

Let

f = kmᵃLᵇFⁿ

where k is a dimensionless constant

=> [T⁻¹] = k[ML⁻¹]ᵃ[L]ᵇ[MLT⁻²]ⁿ

=>  [T⁻¹] = k[Mᵃ⁺ⁿ] [ Lᵇ⁺ⁿ⁻ᵃ] [T⁻²ⁿ]

from the equation we get,

-2n = -1

=> n = 1/2

a+n = 0

=> a = -1/2

b + n -a = 0

=> b + 1/2 + 1/2 = 0

=> b = -1

Hence the formula for frequency

f = k/L x √F/m

Answer 2

⭐《ANSWER》

$\huge\mathfrak\pink {ANSWER}$

↪Actually welcome to the concept of the DIMENSIONAL ANALYSIS

↪Basically we know that, the frequency has the unit As the time inverse,

↪thus the dimension of the frequency is

[ f] = [ T^-1]

↪and thus remaining parameters are

↪[L ] = [ L]

↪[ F ] = [ M L T^-2 ]

↪[ M ] = [ M L^-1]

↪After this , assuming variables a,b,c as powers and equating the coefficents to get the formula