A metal wire of length - 1 - is held between two rigid supports and cooled through a fall of temperature T- For the wire metal- Y - Young-s modulus- - density and - - coefficient of linear expansion- Then the frequency of oscillation of the wire is proportional to

The correct options are A √(Y) B √(α/ρ) D √(T)f=1/l√(T_1/m)=1/l√(YAα T/Aρ)=1/l√(Yα T/ρ) ...

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Standard XII

Mathematics

Greatest Binomial Coefficients

A metal wire ...

Question

A metal wire of length ‘l’ is held between two rigid supports and cooled through a fall of temperature T. For the wire metal, Y = Young's modulus, $ρ$ = density and $α$ = coefficient of linear expansion. Then the frequency of oscillation of the wire is proportional to

\sqrt{Y}

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\sqrt{\frac{α}{ρ}}

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\sqrt{l}

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\sqrt{T}

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Solution

The correct options are
A $\sqrt{Y}$
B $\sqrt{\frac{α}{ρ}}$
D $\sqrt{T}$
$f = \frac{1}{l} \sqrt{\frac{T_{1}}{m}} = \frac{1}{l} \sqrt{\frac{Y A α T}{A ρ}} = \frac{1}{l} \sqrt{\frac{Y α T}{ρ}}$

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