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Byju's Answer

Standard XII

Physics

Young's Modulus of Elasticity

Steel wire of...

Question

Steel wire of length ' $L$ ' at $40^{o} C$ is suspended from the ceiling and then a mass ' $m$ ' is hung from its free end. The wire is cooled down from $40^{o} C$ to $30^{o} C$ to regain its original length $^{'} L^{'}$ . The coefficient of linear thermal expansion of the steel is $10^{- 5} /^{o} C$ , Young's modulus of steel is $10^{11} N / m^{2}$ and radius of the wire is 1 mm. Assume that $L >>$ diameter of the wire. Then the value of ' $m$ ' in kg is nearly

3

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Solution

The correct option is A $3$
We know that
$E = \frac{\frac{F}{A}}{\frac{△ L}{L}}$ ⇒ $\frac{Δ L}{L} = \frac{F}{A E}$ ......(i)
Also
$\frac{Δ L}{L} \propto α Δ T$ .....(ii)
from (i) and (ii)
$\frac{F}{A E} = α Δ T$
⇒ $m g = (α Δ T) A E$
⇒ $m = g α Δ T A E$
= $\frac{10^{- 5} \times 10 \times π \times 10^{- 6} \times 10^{11}}{10}$
= $π \approx 3$

So correct answer is a

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Similar questions

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The correct option is A 3We know thatE=FA△LL⇒ΔLL=FAE......(i)AlsoΔLL∝αΔT.....(ii)from (i) and (ii)FAE=αΔT⇒mg=(αΔT)AE⇒m=gαΔTAE=10−5×10×π×10−6×101110=π≈3 So correct answer is a