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Byju's Answer

Standard XII

Physics

Longitudinal Strain

A steel wire ...

Question

A steel wire of uniform cross-section of $1 m m^{2}$ is heated upto $50^{o} C$ and clamped rigidly at its ends. If temperature of wire falls to $40^{o} C$ , change in tension in the wire is (coefficient of linear expansion of steel is $1.1 \times 10^{- 5} /^{o} C$ and Young's modulus of elasticity of steel is $2 \times 10^{11} N / m^{2}$ )

22 N

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44 N

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88 N

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88 \times 10^{6} N

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Solution

The correct option is A $22 N$
$F = Y A \frac{Δ l}{l} = Y A α Δ θ$
$= 2 \times 10^{11} \times (1 \times 10^{- 6}) \times 1.1 \times 10^{- 5} \times (10) = 22 N$

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A steel wire of uniform cross-section of 1mm2 is heated upto 50oC and clamped rigidly at its ends. If temperature of wire falls to 40oC, change in tension in the wire is (coefficient of linear expansion of steel is 1.1×10−5/oC and Young's modulus of elasticity of steel is 2×1011N/m2)

The correct option is A 22NF=YAΔll=YAαΔθ=2×1011×(1×10−6)×1.1×10−5×(10)=22N

The correct option is A $22 N$
$F = Y A \frac{Δ l}{l} = Y A α Δ θ$
$= 2 \times 10^{11} \times (1 \times 10^{- 6}) \times 1.1 \times 10^{- 5} \times (10) = 22 N$