Two rods A and B of identical dimensions are at a temperature of 30 ° C If A is heated upto 180 ° C and B up to T (measured in ° C ) then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4: 3, then the value of T is

Question

Two rods A and B of identical dimensions are at a temperature of 30 ° C If A is heated upto 180 ° C and B up to T (measured in ° C ) then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4: 3, then the value of T is (A) 230° C (B) 200° C (C) 270° C (D) 250° C

Tardigrade Admin · Accepted Answer

Δ L1=Δ L2 Lα 1× 150=Lα 2× Δ T2 ⇒ Δ T2=(α 1/α 2)× 150=(4/3)× 150=200° C T=200° C+30° C=230° C

$23 0^{\circ} C$

$20 0^{\circ} C$

$27 0^{\circ} C$

$25 0^{\circ} C$

$Δ L_{1} = Δ L_{2}$
$L α_{1} \times 150 = L α_{2} \times Δ T_{2}$
$\Rightarrow Δ T_{2} = \frac{α _{1}}{α _{2}} \times 150 = \frac{4}{3} \times 150 = 20 0^{\circ} C$
$T = 20 0^{\circ} C + 3 0^{\circ} C = 23 0^{\circ} C$

Q. Two rods A and B of identical dimensions are at a temperature of 30∘C If A is heated upto 180∘C and B up to T (measured in ∘C ) then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4:3, then the value of T is

230∘C

200∘C

270∘C

250∘C

ΔL1​=ΔL2​ Lα1​×150=Lα2​×ΔT2​ ⇒ΔT2​=α2​α1​​×150=34​×150=200∘C T=200∘C+30∘C=230∘C

$23 0^{\circ} C$

$20 0^{\circ} C$

$27 0^{\circ} C$

$25 0^{\circ} C$

$Δ L_{1} = Δ L_{2}$
$L α_{1} \times 150 = L α_{2} \times Δ T_{2}$
$\Rightarrow Δ T_{2} = \frac{α _{1}}{α _{2}} \times 150 = \frac{4}{3} \times 150 = 20 0^{\circ} C$
$T = 20 0^{\circ} C + 3 0^{\circ} C = 23 0^{\circ} C$