Question

the frequency of vibration of string is given by f= p/2l [F/m]^1/2.Here p is is the no of segments in the string and l is the length.What is the dimensional formula of m?

Answer 1

Given,
$\nu =\frac{p}{2l}{\left[F/m\right]}^{1/2}$
squaring both sides,
$$\begin{gathered} {\nu }^2=\frac{p^2}{4l^2}\left[\frac{F}{m}\right] \\ m=\frac{p^{2}F}{{\nu }^2\times 4l^2},whereFistheforceand\nu isthefrequency \end{gathered}$$
m = $\frac{{\left[M^0{L}^0{T}^0\right]}^2\left[M^1{L}^1{T}^{-2}\right]}{{\left[M^0{L}^0{T}^{-1}\right]}^2{\left[L\right]}^2}$
On solving, we get the dimensions of m = [M¹L^-1T⁰]