The frequency of vibration of string is given by $f =\frac{p}{2l}\sqrt{\frac{F}{μ}}$. Here $p$ is number of segments in the string and $l$ is the length. The dimension formula for μ will be:

$[M^0LT^{–1}]$ $[M^1L^2T^1]$ $[ML^{–1}T^0]$ $[M^0L^2T^{–1}]$

$[ML^{–1}T^0]$

The correct answer is Option (3) → $[ML^{–1}T^0]$ The dimension of $m=\frac{F}{f^2l^2}=\frac{MLT^{-2}}{T^{-2}L^2}=ML^{-1}$