What is the percentage change in length of 1m iron rod if the temperature change by $100^{\circ}$ C ( $α = 2 \times 10^{- 5} /^{\circ}$ )C

$0.1 %$

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$0.2 %$

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$0.3 %$

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$0.4 %$

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Solution

The correct option is B
$0.2 %$

$l^{'} = l (1 + α Δ T) \Rightarrow l^{'} - l = l \times Δ T \Rightarrow \frac{Δ l}{l} = α Δ T = 2 \times 10^{- 5} \times 100 = 2 \times 10^{- 3}$
% change in length = $\frac{Δ l}{l} \times 100 = 2 \times 10^{- 3} \times 100 = 0.2 %$

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An Iron rod and a copper rod lie side by side. As the temperature is changed, the difference in the lengths of the rods remains constant at a value of 10 cm. Find the lengths at $0^{\circ} C$ . Coefficients of linear expansion of iron and copper are $1.1 \times 10^{- 6} /^{\circ} C$ and $1.7 \times 10^{- 5} /^{\circ} C$ respectively.

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What is the percentage change in length of 1m iron rod if the temperature change by 100∘C (α=2×10−5/∘)C

The correct option is B 0.2% l′=l(1+αΔT)⇒l′−l=l×ΔT⇒Δll=αΔT=2×10−5×100=2×10−3 % change in length = Δll×100=2×10−3×100=0.2%

What is the percentage change in length of 1m iron rod if the temperature change by $100^{\circ}$ C ( $α = 2 \times 10^{- 5} /^{\circ}$ )C

The correct option is B
$0.2 %$

$l^{'} = l (1 + α Δ T) \Rightarrow l^{'} - l = l \times Δ T \Rightarrow \frac{Δ l}{l} = α Δ T = 2 \times 10^{- 5} \times 100 = 2 \times 10^{- 3}$
% change in length = $\frac{Δ l}{l} \times 100 = 2 \times 10^{- 3} \times 100 = 0.2 %$