The frequency of vibration of string is given by v = 2 l p [ m F ] 1/2 Here p is number of segments in the string and l is the length. The dimensional formula for m will be

v = 2 ℓ p [ m F ] 1/2 v 2 = 4 ℓ 2 p m F ⇒ m = 4 ℓ 2 v 2 p 2 F Now, dimensional formula of R.H.S. = L 2 ( T 1 ) 2 MLT − 2 [p will have no dimension as it is an integer] = ML − 1 T 0 So, dimensions of m will be ML − 1 T 0 .

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PhysicsUnit & DimensionMiscellaneousEasy2 minPYQ_2016

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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 and $l$ is the length. The dimensional formula for $m$ will be

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$v = \frac{p}{2 ℓ} [\frac{F}{m}]^{1/2}$ $v^{2} = \frac{p}{4 ℓ ^{2}} \frac{F}{m} \Rightarrow m = \frac{p ^{2} F}{4 ℓ ^{2} v ^{2}}$ Now, dimensional formula of R.H.S. $= \frac{MLT ^{- 2}}{L ^{2} ( \frac{1}{T} ) ^{2}}$ [p will have no dimension as it is an integer] $= ML^{- 1} T^{0}$ So, dimensions of $m$ will be $ML^{- 1} T^{0}$ .

Stream:BITSATSubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2016

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