Question

The frequency of vibration of a string is given by $v=\frac{p}{2l}{\left[\frac{F}{m}\right]}^{\frac{1}{2}}$.

Here $p$ is the number of segments in which the string is divided, $F$ is the tension in the string and $l$ is its length. The dimensional formula for $m$ is:

• A. $M^0{L}^0{T}^0$
• B. ${ML}^{-1}{T}^0$
• C. ${ML}^0{T}^{-1}$
• D. $M^0{LT}^{-1}$

Answer 1

The correct option is B ${ML}^{-1}{T}^0$

$v=\frac{p}{2l}{\left[\frac{F}{m}\right]}^{\frac{1}{2}}$
$T^{-1}=L^{-1}{\left(\frac{M^1{L}^1{T}^{-2}}{m}\right)}^{\frac{1}{2}}$
${\left(L{T}^{-1}\right)}^2=\frac{M^1{L}^1{T}^{-2}}{m}$
${mL}^2{T}^{-2}=M^1{L}^1{T}^{-2}$
$m=M^1{L}^{-1}{T}^0$