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Assuming that the frequency gamma of a vibrating string may depend upon (i) applied force (F) (ii) length (l) (iii) mass per unit lengt (m), prove that gamma prop1/l sqrt(F/m) using dimensional analysis.

Answer» <html><body><p><br/></p>Solution :`gamma prop F^(x) l^(y) m^(z) prop gamma = K F^(x) l^(y) m^(z)` <br/> substitute the dimensional formulae of the above quantities <br/> `[M^(<a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a>)L^(0)T^(-<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)] = [MLT^(-<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)]^(x) [L] [ML^(-1)]^(z)` <br/> `[M^(0)L^(0)T^(-1)] = [M^(x + z)L^(x+y-z)T^(-2x)]` <br/> Comparing the <a href="https://interviewquestions.tuteehub.com/tag/powers-1162174" style="font-weight:bold;" target="_blank" title="Click to know more about POWERS">POWERS</a> of M,L,T on both sides, <br/> `x+z = 0, x+y-z = 0, -2x = -1` <br/> Solving for x,y,z, we get <br/> `x = 1/2``y = -1``z = -1/2` <br/> Substitute x,y,z <a href="https://interviewquestions.tuteehub.com/tag/values-25920" style="font-weight:bold;" target="_blank" title="Click to know more about VALUES">VALUES</a> in equ (1) <br/> `gamma prop F^(1//2) l^(-1) m^(-1//2) :. gamma prop 1/l sqrt(F/m)`</body></html>


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