Question

Two rods $A$ and $B$, of identical dimensions, are at a temperature of ${30}^{\circ }\text{C}$. If $A$ is heated upto ${180}^{\circ }\text{C}$ and $B$ upto $T^{\circ }\text{C}$, then their new lengths are the same. If the ratio of the coefficients of linear expansion of $A$ and $B$ is $4:3$, the value of $T$ is :

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

Answer 1

The correct option is A ${230}^{\circ }\text{C}$

As the initial and final lengths of the rods are the same, so, the change in length in both rods will also be the same,

i.e. $\Delta l_A=\Delta l_B$

So, $l_A{\alpha }_A(\Delta \theta {)}_A=l_B{\alpha }_B(\Delta \theta {)}_B$

$\Rightarrow \frac{{\alpha }_A}{{\alpha }_B}=\frac{\Delta {\theta }_B}{\Delta {\theta }_A}(\because l_A=l_B)$

$\Rightarrow \frac{4}{3}=\frac{T_B-30}{180-30}$

$\therefore T_B={230}^{\circ }\text{C}$

Hence, $\left(A\right)$ is the correct answer.