The frequency of vibration of string is given by $ϑ = \frac{n}{2 l} {[\frac{F}{λ}]}^{1 / 2}$ , here p is number of segments in the string, l is the length and F is the tension in the string. The dimensional formula for $λ$ will be

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

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

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

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

answer is C.

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Detailed Solution

$v = \frac{P}{2 l} {[\frac{F}{m}]}^{1 / 2} \Rightarrow v^{2} = \frac{P^{2}}{4 l^{2}} [\frac{F}{m}] ∴ m \propto \frac{F}{l^{2} v^{2}}$

$\Rightarrow [m] = [\frac{M L T^{- 2}}{L^{2} T^{- 2}}] = [M L^{- 1} T^{0}]$

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