Physics

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

##### SOLUTION
$\nu=\cfrac{1}{2l}\sqrt{\cfrac{T}{M}}$
Where $T$ Tension.
$m=$ Mass per unit Length.
$l=$Length.
$\nu=$ Frequency.
Dimension of $T=[MLT^{-2}]$
Dimension of $m=[ML^{-1}]$
Dimension of $l=[L]$
Dimension of $\nu=[T^{-1}]$
$\because$ L.H.S Should be equal to R.H.S
L.H.S$=[T^{-1}]$
R.H.S $=\cfrac{M^{\dfrac{1}{2}}L^{\dfrac{1}{2}}T^{-1}}{M^{\dfrac{1}{2}}L^{\dfrac{-1}{2}}L}$
$=\cfrac{T^{-1}}{L^{\dfrac{1}{2}}L^{\dfrac{-1}{2}}}$
$\therefore$ L.H.S $=$ R.H.S

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Subjective Medium Published on 18th 08, 2020
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