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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