The frequency n of vibrations of uniform string of length l and stretched with a force F is given by n = $\frac{p}{2 l} \sqrt{\frac{F}{m}}$ ,
where p is the number of segments of the vibrating string and m is a constant of the string. What are the dimensions of m?

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M L^-3 T⁰

M L^-1 T⁰

M L^-2T⁰

M L^{- 1} T^-1

answer is D.

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Detailed Solution

Squaring both sides of the given relation, we get:

$n^{2} = \frac{p^{2}}{4 l^{2}} . \frac{F}{m} or m = \frac{p^{2} F}{4 l^{2} n^{2}} ∴ [m] = \frac{[F]}{[l^{2}] [n^{2}]} [∵ p is a dimesnionless number] = \frac{{MLT}^{- 2}}{L^{2} \times {(T^{- 1})}^{2}} = {ML}^{- 1} T^{0}$

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