NEET Physics Thermometry, Calorimetry & Thermal Expansion NEET PYQ-Thermometry, Calorimetry and Thermal Expansion

Coefficient of linear expansion of brass and steel rods are \[{{\alpha }_{1}}\] and \[{{\alpha }_{2}}\]. Lengths of brass and steel rods are \[{{\ell }_{1}}\] and \[{{\ell }_{.2}}\] respectively. If \[({{\ell }_{2}}-{{\ell }_{1}})\] is maintained same at all temperatures, which one of the following relations holds good?                                     [NEET - 2016]

A) \[{{\alpha }_{1}}{{\ell }_{2}}={{\alpha }_{2}}{{\ell }_{1}}\]

B)      \[{{\alpha }_{1}}\ell _{2}^{2}={{\alpha }_{2}}\ell _{1}^{2}\]

C) \[\alpha _{1}^{2}{{\ell }_{2}}=\alpha _{2}^{2}{{\ell }_{1}}\]

D)      \[{{\alpha }_{1}}{{\ell }_{1}}={{\alpha }_{2}}{{\ell }_{2}}\]

Correct Answer: D

Solution :

[d] Change in length for both rods should be same

\[\Delta {{\ell }_{1}}=\Delta {{\ell }_{2}}\]

\[{{\ell }_{1}}{{\alpha }_{1}}\Delta T={{\ell }_{2}}{{\alpha }_{2}}\Delta T\]

\[{{\ell }_{1}}{{\alpha }_{1}}={{\ell }_{2}}{{\alpha }_{2}}\]