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

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0.5

0.7

2.3

3.6

answer is D.

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Detailed Solution

$v = \sqrt{\frac{T}{M}} = {[\frac{m' g}{M / ℓ}]}^{1 / 2} = {[\frac{m' ℓg}{M}]}^{1 / 2}$

It follows from here, $\frac{Δv}{v} = \frac{1}{2} [\frac{Δm'}{m'} + \frac{Δℓ}{ℓ} + \frac{ΔM}{M}]$

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

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

Percentage error in the measurement = 3.6

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