Question

The velocity (v) of vibration of wire under tension depends upon the tension (T) mass per unit length (m). Using dimensional analysis, obtain the dependence of velocity on these quantities.

Answer 1

Hey Dear,

◆ Answer -

v = √(T/m)

● Explaination -

First we'll write down known dimensions of given quantities.

[v] = [L1T-1]

[m] = [M1L-1]

[T] = [L1M1T-2]

Let velocity of vibration of wire be expressed by following equation.

v = m^x.T^y

According to principle of homogeneity of dimensions,

[v] = [m]^y.[T]^y

[L1T-1] = [L-1M1]^x.[L1M1T-2]^y

[L1T-1] = [L^(-x+y).M^(x+y).T^(-2y)]

Comparing indexes on two sides -

-x+y = 1

x+y = 0

-2y = -1

Solving these equations,

x = -1/2

y = 1/2

Putting this values in original equation,

v = m^-½.T^½

v = √(T/m)

Thanks dear...