Question

The frequency (n) of vibration of a string is given as $n=\frac{1}{2l}\sqrt{\frac{T}{m}}$, where T is tension and l is the length of vibrating string, then the dimensional formula is

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

Answer 1

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

Given, $n=\frac{1}{2l}\sqrt{\frac{T}{M}}$

Squaring both sides,

$n^2=\frac{1}{4l^2}\frac{T}{m}$

$m=\frac{T}{4l^2{n}^2}$........................(1).

Here, $T=F=ma$, means tension is kind of force.

so, dimensional formula for T will be $M^1{L}^1{T}^{-2}$

Thus dimensional formula using (1),

$M=\frac{M^1{L}^1{T}^{-2}}{M^0{L}^2{T}^0\ast M^0{L}^0{T}^{-2}}$

$M=M^1{L}^{-1}{T}^0$