Question

The frequency of vibration of string is given by
$V=\frac{p}{2l}\left[\frac{F}{m}\right]^{1/2}$ Here p is number of segments in the string and $l$ is the length. The dimensional formula for m will be

• A. $\left[M^{0}LT^{-1}\right]$
• B. $\left[ML^{0}T^{-1}\right]$
• C. $\left[ML^{-1}T^{0}\right]$
• D. $\left[M^{0}L^{0}T^{0}\right]$

Answer 1

Answer: (C)

$v=\frac{p}{2l}\left[\frac{F}{M}\right]^{1/2}$
$\Rightarrow v^{2}=\frac{P_{2}}{4l^{2}}\left[\frac{F}{m}\right]$
$\therefore m\propto\frac{F}{l^{2}V^{2}}$
$\Rightarrow \left[m\right]=\left[\frac{MLT^{-2}}{L^{2}T^{-2}}\right]$
$=\left[ML^{-1}T^{0}\right]$