The frequency of vibration of a string is giv | vedclass

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(C) The given formula is $
u = \frac{p}{2l} \left[ \frac{F}{m} ight]^{1/2}$.Squaring both sides,we get $
u^2 = \frac{p^2}{4l^2} \left[ \frac{F}{m}

Vedclass · Accepted Answer

$[M L^{-1} T^0]$

Vedclass · Answer

(C) The given formula is $
u = \frac{p}{2l} \left[ \frac{F}{m} ight]^{1/2}$.Squaring both sides,we get $
u^2 = \frac{p^2}{4l^2} \left[ \frac{F}{m} ight]$.Rearranging for $m$,we have $m = \frac{p^2 F}{4l^2 
u^2}$.Since $p$ is a dimensionless number,the dimensional formula for $m$ is $[m] = \frac{[F]}{[l^2][
u^2]}$.Substituting the dimensions: $[F] = [M L T^{-2}]$,$[l] = [L]$,and $[
u] = [T^{-1}]$.$[m] = \frac{[M L T^{-2}]}{[L^2][T^{-1}]^2} = \frac{[M L T^{-2}]}{[L^2][T^{-2}]} = [M L^{1-2} T^{-2+2}] = [M L^{-1} T^0]$.

The frequency of vibration of a string is given by $\nu = \frac{p}{2l} \left[ \frac{F}{m} \right]^{1/2}$. Here $p$ is the number of segments in the string,$l$ is the length,and $F$ is the tension. The dimensional formula for $m$ will be:

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