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Q.

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

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a

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

b

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

c

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

d

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

answer is C.

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Detailed Solution

${[T]}^{- 1} = {[m]}^{- 1 / 2} {[M]}^{1 / 2} {[L]}^{- 1 / 2} {[T]}^{- 1} {[m]}^{- 1 / 2} = {[M]}^{- 1 / 2} {[L]}^{1 / 2} [m] = [M] {[L]}^{- 1}$

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