Physics And Measurement Question 302

Question: The frequency (f) of a wire oscillating with a length , in p loops, under a tension T is given by f=P2Tμ where μ= linear density of the wire. If the error made in determining length, tension and linear density be 1%, -2% and 4%, then find the percentage error in the calculated frequency

Options:

A) - 4%

B) - 2%

C) - 1%

D) - 5%

Show Answer

Answer:

Correct Answer: A

Solution:

[a] Given f=ρ2Tμ

Taking log of both sides logf=log(p2)log+12logT12logμ

Differentiating partially on both sides,

dff=0d+12dTT12dμμ

or dff×100=(d×100)+(12dTT×100)(12dμμ×100)

=(1)+12(2)12(4)=112=4



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