First slide

Dimensions of physical quantities

Question

The frequency ( $n$ ) of vibration of a string is given as $n = \frac{1}{2 l} \sqrt{\frac{T}{m}}$ , where $T$ is tension and $l$ is the length of vibrating string, then the dimensional formula of $m$ is

Moderate

A

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

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

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

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

Solution

$\begin{matrix} n = \frac{1}{2 l} \sqrt{\frac{T}{m}} \\ \Rightarrow n^{2} = \frac{1}{4 l^{2}} \frac{T}{m} \\ \Rightarrow m = \frac{T}{4 l^{2} n^{2}} = [\frac{M L T^{- 2}}{L^{2} \times T^{- 2}}] = [M^{1} L^{- 1} T^{0}] \end{matrix}$

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