> Q. The velocity of a transverse wave in a string is directly proportional to $ sqrt T $ and inversely proportional to $ sqrt mu $ . In a measurement, the mass applied at the end of string is $ 3.0 ,g $ , length of string is $ 1 ,m $ and mass of string is $ 5 ,g $ . If possible error in measuring mass is $ 0.1 ,g $ and that of length is $ 1 ,mm $ , the percentage error in measurement of velocity is – LIVE ANSWER TODAY

Q. The velocity of a transverse wave in a string is directly proportional to $ sqrt T $ and inversely proportional to $ sqrt mu $ . In a measurement, the mass applied at the end of string is $ 3.0 ,g $ , length of string is $ 1 ,m $ and mass of string is $ 5 ,g $ . If possible error in measuring mass is $ 0.1 ,g $ and that of length is $ 1 ,mm $ , the percentage error in measurement of velocity is

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The velocity of a transverse wave in a string is directly proportional to $ sqrt T $ and inversely proportional to $ sqrt mu $ . In a measurement, the mass applied at the end of string is $ 3.0 ,g $ , length of string is $ 1 ,m $ and mass of string is $ 5 ,g $ . If possible error in measuring mass is $ 0.1 ,g $ and that of length is $ 1 ,mm $ , the percentage error in measurement of velocity is

Solution:

According to the question,

$vproptosqrt{frac{T}{mu}} = k sqrt{frac{T}{mu}} $

As $mu = frac{M}{L}$ and $T = m’ g $

$ Rightarrow v = ksqrt{frac{TL}{M}} = k sqrt{frac{m’gL}{M}} $

$Rightarrow frac{Delta v}{v} = frac{1}{2} frac{Delta m’}{m’} + frac{1}{2} frac{Delta L}{L} + frac{1}{2} frac{Delta M}{M}$

$= frac{1}{2}times frac{0.1}{5} + frac{1}{2} times frac{1times 10^{-3}}{1} + frac{1}{2} times frac{0.1}{3}$

$= 0.01 + 0.0005 + 0.016$

$ = 0.0271 = 2.7 %$

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