The frequency of vibration of string is given by v=(p/2l)[ (F/m) ]1/2 Here, p is the 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 the 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 Squaring the equation on either side, we have v2=(p2/4l2)( (F/m) ) m=(P2F/4l2v2) [m]=([MLT-2]/[L2][T-1]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 the number of segments in the string and $l$ is the length. The dimensional formula for $m$ will be

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

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

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

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

$v = \frac{p}{2 l} [\frac{F}{m}]^{1/2}$
Squaring the equation on either side, we have
$v^{2} = \frac{p ^{2}}{4 l ^{2}} (\frac{F}{m})$
$m = \frac{P ^{2} F}{4 l ^{2} v ^{2}}$
$[m] = \frac{[ M L T ^{- 2} ]}{[ L ^{2} ] [ T ^{- 1} ] ^{2}} = [M L^{- 1} T^{0}]$

Q. The frequency of vibration of string is given by v=2lp​[mF​]1/2 Here, p is the 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]