Question

The frequency $\left(n\right)$ 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 magnitude of summation of powers of $M$ and $L$ in the dimensional formula of $m$ is

Answer 1

$n=\frac{1}{2l}\sqrt{\frac{T}{m}}\Rightarrow n^2=\frac{1}{4l^2}\frac{T}{m}$
$m=\frac{T}{4l^2{n}^2}=\left[\frac{ML{T}^{-2}}{L^2\times T^{-2}}\right]=\left[M{L}^{-1}\right]$