The frequency of vibration of string is given by V=(p/2l)[(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

Question

The frequency of vibration of string is given by V=(p/2l)[(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 (A) [M0LT-1] (B) [ML0T-1] (C) [ML-1T0] (D) [M0L0T0]

Tardigrade Admin · Accepted Answer

v=(p/2l)[(F/M)]1/2 ⇒ v2=(P2/4l2)[(F/m)] ∴ m propto(F/l2V2) ⇒ [m]=[(MLT-2/L2T-2)] =[ML-1T0]

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

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

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

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

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

$v = \frac{p}{2 l} [\frac{F}{M}]^{1/2}$
$\Rightarrow v^{2} = \frac{P _{2}}{4 l ^{2}} [\frac{F}{m}]$
$∴ m \propto \frac{F}{l ^{2} V ^{2}}$
$\Rightarrow [m] = [\frac{M L T ^{- 2}}{L ^{2} T ^{- 2}}]$
$= [M L^{- 1} T^{0}]$

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

[M0LT−1]

[ML0T−1]

[ML−1T0]

[M0L0T0]