Question

The frequency (n) of vibration 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. $\left[M^{\circ }{L}^1{T}^1\right]$
• B. $\left[M^{\circ }{L}^{\circ }{T}^{\circ }\right]$
• C. $\left[M^1{L}^{-1}{T}^{\circ }\right]$
• D. $\left[M{L}^{\circ }{T}^0\right]$

Answer 1

The correct option is C $\left[M^1{L}^{-1}{T}^{\circ }\right]$

The correct answer is C.

Given,

$f=\frac{1}{2l}\sqrt{\frac{T}{m}}$

Here, $f$ is the frequency, $T$ is the tension in the string.

Squaring both sides then we get,

$f^2=\frac{1}{4l^2}\frac{T}{m}$

$m=\frac{T}{4l^2{f}^2}$

Here,

$T=F=ma$

So,

$T=M^1{L}^1{T}^{-2}$

Thus, the dimensional formula is

$m=\frac{M^1{L}^1{T}^{-2}}{M^0{L}^2{T}^0\times M^0{L}^0{T}^{-2}}$

=$M^1{L}^{-1}{T}^0$