Question

Two rods $A$ and $B$ of identical dimensions are at a temperature of $30{ }^{\circ} C$ If $A$ is heated upto $180{ }^{\circ} C$ and $B$ up to $T$ (measured in ${ }^{\circ} C$ ) 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. $230^\circ C$
• B. $200^\circ C$
• C. $270^\circ C$
• D. $250^\circ C$

Answer 1

Answer: (A)

$\Delta L_{1}=\Delta L_{2}$
$L\alpha _{1}\times 150=L\alpha _{2}\times \Delta T_{2}$
$\Rightarrow \, \, \Delta T_{2}=\frac{\alpha _{1}}{\alpha _{2}}\times 150=\frac{4}{3}\times 150=200^\circ C$
$T=200^\circ C+30^\circ C=230^\circ C$