The table gives the initial length $l_{0}$ , change in temperature $Δ T$ and change in length $Δ l$ of four rods. Which rod has greatest coefficient of linear expansion
$\begin{matrix} Rod & l_{0} (m) & Δ T (^{\circ} C & Δ l (m) A_{1} & 1 & 100 & 1 A_{2} & 1 & 100 & 2 A_{3} & 1.5 & 50 & 3 A_{4} & 2.5 & 20 & 4 \end{matrix}$

A_{1}

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A_{2}

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A_{3}

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A_{4}

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Solution

The correct option is D $A_{4}$
$Δ l = l_{0} α Δ T \Rightarrow α = \frac{Δ l}{l_{0} Δ T}$
$α_{1} = \frac{1}{1 \times 100} = 10^{- 2}$
$α_{2} = \frac{2}{100} = 2 \times 10^{- 2}$
$α_{3} = \frac{3}{1.5 \times 50} = 4 \times 10^{- 2}$
$α_{4} = \frac{4 \times 5}{2.5 \times 20.5} = 8 \times 10^{- 2} (maximum)$

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Similar questions

Q. The table gives the initial length

l_{0}

, change in temperature

Δ T

and change in length

Δ l

of four rods. Which rod has greatest coefficient of linear expansion

Q. The table gives the initial length

l_{0}

, change in temperature

Δ T

and change in length

Δ l

of four rods. Which rod has greatest coefficient of linear expansion

\begin{matrix} Rod & l_{0} (m) & Δ T (^{\circ} C & Δ l (m) A_{1} & 1 & 100 & 1 A_{2} & 1 & 100 & 2 A_{3} & 1.5 & 50 & 3 A_{4} & 2.5 & 20 & 4 \end{matrix}

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

Q. The table below lists the original length, the coefficient of linear expansion, and the original temperature for five different metal bars. Heat is added to all the bars so that they change temperature by the same amount.
What is the correct order for the amount of increase in length for the bars, greatest first?

Metal Rod Number >	$1$	$2$	$3$	$4$	$5$
Original Length	$5.0 m$	$2.0 m$	$3.0 m$	$4.0 m$	$1.0 m$
Coefficient of Linear Expansion	$15 \times 10^{- 6} K^{- 1}$	$35 \times 10^{- 6} K^{- 1}$	$20 \times 10^{- 6} K^{- 1}$	$20 \times 10^{- 6} K^{- 1}$	$65 \times 10^{- 6} K^{- 1}$
Original Temperature	$25^{\circ} C$	$35^{\circ} C$	$15^{\circ} C$	$20^{\circ} C$	$10^{\circ} C$

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The table gives the initial length l0, change in temperature ΔT and change in length Δl of four rods. Which rod has greatest coefficient of linear expansion Rodl0(m)ΔT(∘CΔl(m)A111001A211002A31.5503A42.5204

The correct option is D A4Δl=l0αΔT⇒α=Δll0ΔT α1=11×100=10−2 α2=2100=2×10−2 α3=31.5×50=4×10−2 α4=4×52.5×20.5=8×10−2(maximum)