Question

Check the correctness of equation
$v=\frac{1}{2l}\sqrt{\frac{T}{M}}$

Answer 1

$\nu =\frac{1}{2l}\sqrt{\frac{T}{M}}$

Where $T$ Tension.

$m=$ Mass per unit Length.

$l=$Length.

$\nu =$ Frequency.

Dimension of $T=\left[ML{T}^{-2}\right]$

Dimension of $m=\left[M{L}^{-1}\right]$

Dimension of $l=\left[L\right]$

Dimension of $\nu =\left[T^{-1}\right]$

$\because$ L.H.S Should be equal to R.H.S

L.H.S$=\left[T^{-1}\right]$

R.H.S $=\frac{M^{\frac{1}{2}}{L}^{\frac{1}{2}}{T}^{-1}}{M^{\frac{1}{2}}{L}^{\frac{-1}{2}}L}$

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

$\therefore$ L.H.S $=$ R.H.S