Two rods A and B of identical dimensions are at temperature 30°C. If A is heated upto 180°C and B upto T°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 temperature 30°C. If A is heated upto 180°C and B upto T°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) 270° C (B) 230° C (C) 250° C (D) 200° C

Tardigrade Admin · Accepted Answer

Δℓ1 = Δℓ2 ℓα1 Δ T1 =ℓα2Δ T2 (α1/α2) = (Δ T1/Δ T2) (4/3) = (T- 30/180-30) T = 230°C

Q. Two rods $A$ and $B$ of identical dimensions are at temperature $3 0^{\circ} C$ . If $A$ is heated upto $18 0^{\circ} C$ and $B$ upto $T^{\circ} C$ , 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 :

$27 0^{\circ} C$

$23 0^{\circ} C$

$25 0^{\circ} C$

$20 0^{\circ} C$

$Δ ℓ_{1} = Δ ℓ_{2}$
$ℓ α_{1} Δ T_{1} = ℓ α_{2} Δ T_{2}$
$\frac{α _{1}}{α _{2}} = \frac{Δ T _{1}}{Δ T _{2}}$
$\frac{4}{3} = \frac{T - 30}{180 - 30}$
$T = 23 0^{\circ} C$

Q. Two rods A and B of identical dimensions are at temperature 30∘C. If A is heated upto 180∘C and B upto T∘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 :

270∘C

230∘C

250∘C

200∘C