Q. 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 $T = 3.0$ kgf, mass of string is 2.5 g 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
Explanation
$v = \sqrt{\frac{T}{m}} = \left\lbrack \frac{m^{'}g}{\frac{M}{t}} \right\rbrack^{1/2} = \left\lbrack \frac{m'lg}{M} \right\rbrack^{1/2}$ It follows from here, $\frac{\mathrm{\Delta}v}{v} = \frac{1}{2}\left\lbrack \frac{\mathrm{\Delta}m'}{m} + \frac{\mathrm{\Delta}l}{l} + \frac{\mathrm{\Delta}M}{M} \right\rbrack$ $= \frac{1}{2}\left\lbrack \frac{0.1}{3.0} + \frac{0.001}{1.000} + \frac{0.1}{2.5} \right\rbrack$ $= \frac{1}{2}\lbrack 0.03 + 0.001 + 0.04\rbrack$ $= 0.036$ Percentage error in the measurement=3.6
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.