Question

The frequency $n$ of vibrations of a string is given as $n=\frac{1}{2l}\sqrt{\frac{T}{m}}$ where $T$ is tension and $l$ is the length of vibrating string. Then the dimensional formula for $m$ is

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

Answer 1

Answer: (C)

$n=\frac{1}{2l}\sqrt{\frac{T}{m}}\Rightarrow n^{2}=\frac{1}{4l^{2}} \frac{T}{m}$
$\Rightarrow m=\frac{T}{4l^{2}n^{2}}=\left[\frac{MLT^{-2}}{L^{2}\times T^{-2}}\right]=\left[ML^{-1}\right]$