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Q.

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

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a

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

b

$[{ML}^{0} T^{- 1}]$

c

$[{ML}^{- 1} T^{0}]$

d

$[M^{0} {LT}^{- 1}]$

answer is C.

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Detailed Solution

Given, $f = \frac{p}{2 l} {[\frac{F}{m}]}^{1 / 2}$

Squaring the equation on either side, we have

$f^{2} = \frac{p^{2}}{4 l^{2}} (\frac{F}{m}) \Rightarrow m = \frac{p^{2} F}{4 l^{2} f^{2}}$

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

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