Q 11-10-116JEE MainJEE Main 2019 (11 Jan, Shift 2)Easy
Two rods A and B of identical dimensions are at temperature $30^\circ$C. If A is heated up to $180^\circ$C and B up to $T^\circ$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
Answer: (A) $230^\circ$C
Equal original lengths and equal final lengths mean equal expansions:
$$\alpha_A(180 - 30) = \alpha_B(T - 30) \Rightarrow T - 30 = \frac43\times150 = 200 \Rightarrow T = 230^\circ\text{C}$$
Solution by Sreeraj P, M.Sc Physics