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

Put the dimensions for each physical quantity in the given relation. Given,

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}]

\Rightarrow m = \frac{p ^{2} F}{4 l ^{2} v}

Putting the dimensions of equations on RHS,
we get

F = [M L T^{- 2}], l = [L], v = [T^{- 1}],

p

being a number is dimensionless, we have

[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
$v = \frac{P}{2 l} [\frac{F}{m}]^{1/2}$
Here $p$ is number of segments in the string and $l$ is the length. The dimensional formula for $m$ will be:

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

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

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

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

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]

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:

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

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

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

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