The frequency of vibration of string is given by $\nu =\frac{p}{2l}{\left[\frac{F}{m}\right]}^{1/2}$. Here p is number of segments in the string and l is the length. The dimensional formula for m will be

(1) $\left[{M}^{0}L{T}^{-1}\right]$

(2) $\left[M{L}^{0}{T}^{-1}\right]$

(3) $\left[M{L}^{-1}{T}^{0}\right]$

(4) $\left[{M}^{0}{L}^{0}{T}^{0}\right]$

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#1 | Basic Concepts & Examples
#2 | Dimensional Analysis : Remaining

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Dimensions

(3) $\nu =\frac{P}{2l}{\left[\frac{F}{m}\right]}^{1/2}$$⇒{\nu }^{2}=\frac{{P}^{2}}{4{l}^{2}}\left[\frac{F}{m}\right]\therefore m\propto \frac{F}{{l}^{2}{\nu }^{2}}$

$⇒\left[m\right]=\left[\frac{ML{T}^{-2}}{{L}^{2}{T}^{-2}}\right]=\left[M{L}^{-1}{T}^{0}\right]$

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