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 $1.000m$ then the percentage error in the measurement of velocity is

• A. $0.5$
• B. $0.7$
• C. $2.3$
• D. $3.6$

Answer 1

The correct option is D $3.6$

$v=\sqrt{\frac{T}{m}}={\left[\frac{m^{\prime }g}{\frac{M}{l}}\right]}^{1/2}={\left[\frac{m^{\prime }lg}{M}\right]}^{1/2}$

It follows from here,

$\frac{\Delta v}{v}=\frac{1}{2}[\frac{\Delta m^{\prime }}{m^{\prime }}+\frac{\Delta l}{l}+\frac{\Delta M}{M}]$

$=\frac{1}{2}[\frac{0.1}{3.0}+\frac{0.001}{1.000}+\frac{0.1}{2.5}]$

$=\frac{1}{2}[0.03+0.001+0.04]=0.036$

Percentage error in the measurement $=0.36\times 100=3.6$