Question

The frequency of vibration of a string is given by $f=\frac{n}{2L}\sqrt{\frac{T}{m}}$, where $T$ is tension in the string, $L$ is the length, $n$ is number of harmonics. The dimensional formula for $m$ is

• A. $\left[M^{0}LT\right]$
• B. $\left[M^1{L}^{-1}{T}^{-1}\right]$
• C. $\left[M^1{L}^{-1}{T}^0\right]$
• D. $\left[M^{0}L{T}^{-1}\right]$

Answer 1

The correct option is C $\left[M^1{L}^{-1}{T}^0\right]$

$\left[Tension\right]=\left[T\right]=\left[M^1{L}^1{T}^{-2}\right]$
Arranging the equation gives, $m=\frac{n^{2}T}{4f^2{L}^2}$
So, $\left[m\right]=\frac{\left[ML{T}^{-2}\right]}{T^{-2}{L}^2}=\left[M^1{L}^{-1}{T}^0\right]$