Question

The velocity of transverse wave in a string is $v=\sqrt{\frac{T}{M}}$ where $T$ is the tension in the string and $M$ is mass per unit length. If $T=3.0kgf$, mass of string is $2.5g$ and length of string is $1.00m$, then the percentage error in the measurement of velocity is

• A. 0.5
• B. 0.7
• C. 2.3
• D. 3.6

Answer 1

Answer: (D)

$v=\sqrt{\frac{T}{m}}={\left[\frac{m^{\prime }g}{M/l}\right]}^{1/2}={\left[\frac{m^{\prime }lg}{M}\right]}^{1/2}$
It follows from here, $\frac{\Delta v}{v}=\frac{1}{2}\left[\frac{\Delta m^{\prime }}{m}+\frac{\Delta l}{l}+\frac{\Delta M}{M}\right]$
$=\frac{1}{2}\left[\frac{0.1}{3.0}+\frac{0.01}{1.000}+\frac{0.1}{2.5}\right]$
$=\frac{1}{2}[0.03+0.001+0.04]=0.036$
Percentage error in the measurement $=3.6$