Question

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

• A. $270^{\circ} C$
• B. $230^{\circ} C$
• C. $250^{\circ} C$
• D. $200^{\circ} C$

Answer 1

Answer: (B)

$\Delta\ell_{1} = \Delta\ell_{2}$
$ \ell\alpha_{1} \Delta T_{1 } =\ell\alpha_{2}\Delta T_{2} $
$ \frac{\alpha_{1}}{\alpha_{2}} = \frac{\Delta T_{1}}{\Delta T_{2}} $
$ \frac{4}{3} = \frac{T- 30}{180-30} $
$ T = 230^{\circ}C$