Two rods A and B of identical dimensions are at temperature $30^{\circ} \mathrm{C}$. If a heated upto $180^{\circ} \mathrm{C}$ and B upto $\mathrm{T}^{\circ} \mathrm{C}$, 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:

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Heat & Thermodynamics

Two rods A and B of identical dimensions are at temperature

3 0^{\circ} C

. If a 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

4 : 3

, then the value of

T

is:

Answer: (A)

Both rods start at

3 0^{\circ}

C with identical lengths and end up equally long, so their increases in length must match:

ℓ α_{A} Δ T_{A} = ℓ α_{B} Δ T_{B}

, which gives

\frac{α _{A}}{α _{B}} = \frac{Δ T _{B}}{Δ T _{A}}

. Rod A is heated through

Δ T_{A} = 180 - 30 = 15 0^{\circ}

C, while rod B is heated through

T - 30

. Using

\frac{α _{A}}{α _{B}} = \frac{4}{3}

\frac{4}{3} = \frac{T - 30}{150}

, so

T - 30 = 200

and

T = 23 0^{\circ}

JEE Main · 2019 · 11 Jan 2019 · Shift 2 · Single correct option