Question

Two rods A and B of identical dimensions are at temperature ${30}^o$C. If A is heated upto ${180}^o$C and B upto $T^o$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. ${270}^o$C
• B. ${230}^o$C
• C. ${250}^o$C
• D. ${200}^o$C

Answer 1

Answer: (B)

${230}^o$C

$\Delta l_1=\Delta l_2$
$l{\alpha }_1\Delta T-1=l{\alpha }_2\Delta T_2$
$\frac{{\alpha }_1}{{\alpha }_2}=\frac{\Delta T_1}{\Delta T_2}$
$\frac{4}{3}=\frac{T-30}{180-30}$
$T={230}^o$C.