The table gives the initial length l0- change in temperature - T and change in length - l of four rods- Which rod has greatest coefficient of linear expansion- Rod l0 m - T-C - lm- A1 1 100 1- A2 1 100 2- A3 1-5 50 3- A4 2-5 20 4- -

Δ l = l _0αΔ T ⇒α = Δ ll _0Δ T α_1 = 11 × 100 = 10^ 2 α_2 = 2100 = 2 × 10^ 2 α_3 = 31.5 × 50 = 4 × 10^ 2 α_4 = 4 × 52.5 × 20.5 = 8 × 10^ 2 (maximum) ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Physics

Thermal Expansion

The table giv...

Question

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}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A_{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A_{4}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

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

Suggest Corrections

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}

Q. Two elastic rods are joined between fixed supports as shown in figure. Condition for no change in the lengths of the individual rods with increase in temperature -
[Given

α \to

linear expansion coefficient,

A \to

area of cross-section of rod,

Y \to

Young's modulus and

L \to

length of rod]

Q. If two rods of length

L

and

2 L

having coefficients of linear expansion

α

and

2 α

respectively are connected so that total length becomes

3 L

, the average coefficient of linear expansion of the composition rod equals:

Q. Two rods of length

L_{1}

and

L_{2}

are welded together to make a composite rod of length

(L_{1} + L_{2})

. If the coefficients of linear expansion of the rod are

α_{1}

and

α_{2}

respectively, the effective coefficient of linear expansion of the composite rod will be

Join BYJU'S Learning Program

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)