Question

The coefficient of linear expansion of brass and steel are ${\alpha }_1$ and ${\alpha }_2$. If we take a brass rod of length $L_1$ and steel rod of length $L_2$ at $0^{\circ }C$, their difference in length $(L_2-L_1)$ will remain the same at any temperature if

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Difference in lengths of rods will remain same if expansion is same in both the rods. If expansion in first rod is $l_1=L_1{\alpha }_1\Delta \theta$ and expansion in second rod is $l_2=L_2{\alpha }_2\Delta \theta$ then $L_1{\alpha }_1\Delta \theta =L_2{\alpha }_2\Delta \theta$ $\therefore L_1{\alpha }_1=L_2{\alpha }_2$