A metallic wire of length l is held between two rigid supports- If the wire is cooled through a temperature t- Y -Young-s modulus of elasticity of wire- - - density- - - thermal coefficient linear expansion- Then the frequency of oscillation is proportional to-

The correct options are A 1l B √(αρ) C √(Y) D √(t) We know that f = 12l√(Tμ) where T is tension and μ mass per unit leng ...

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Byju's Answer

Standard XII

Physics

Young's Modulus of Elasticity

A metallic wi...

Question

A metallic wire of length l is held between two rigid supports. If the wire is cooled through a temperature t. (Y $=$ Young's modulus of elasticity of wire, $ρ =$ density, $α =$ thermal coefficient linear expansion). Then the frequency of oscillation is proportional to.

\frac{1}{l}

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\sqrt{Y}

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\sqrt{\frac{α}{ρ}}

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\sqrt{t}

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Solution

The correct options are
A $\frac{1}{l}$
B $\sqrt{\frac{α}{ρ}}$
C $\sqrt{Y}$
D $\sqrt{t}$
We know that $f = \frac{1}{2 l} \sqrt{\frac{T}{μ}}$
where $T$ is tension and $μ$ mass per unit length
Now, $f = \frac{1}{2 l} \sqrt{\frac{T}{ρ A}}$
Now, $T / A$ is stress and starin, $Δ l / l = α t$
stress = $Y$ strain
$T / A = Y α t$
$∴ f = \frac{1}{2 l} \sqrt{\frac{Y α t}{ρ}}$

$A L L A N W E R S A R E C O R R E C T$

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A metallic wire of length l is held between two rigid supports. If the wire is cooled through a temperature t. (Y=Young's modulus of elasticity of wire, ρ= density, α= thermal coefficient linear expansion). Then the frequency of oscillation is proportional to.

The correct options are A 1l B √αρ C √Y D √tWe know that f=12l√Tμwhere T is tension and μ mass per unit lengthNow, f=12l√TρANow, T/A is stress and starin,Δl/l=αtstress = Y strainT/A=Yαt∴f=12l√YαtρALL ANWERS ARE CORRECT

A metallic wire of length l is held between two rigid supports. If the wire is cooled through a temperature t. (Y $=$ Young's modulus of elasticity of wire, $ρ =$ density, $α =$ thermal coefficient linear expansion). Then the frequency of oscillation is proportional to.