Question

The coefficient of linear expansion of steel and brass are $11\times {10}^{-6}{/}^{\circ }Cand19\times {10}^{-6}{/}^{\circ }C$ respectively. If their difference in lengths at all temperatures has to kept constant at 30 cm, their lengths at $0^{\circ }C$ should be

• A. 71.25 cm and 41.25 cm
• B. 82 cm and 52 cm
• C. 92 cm and 62 cm
• D. 62.25 cm and 32.25 cm

Answer 1

The correct option is A 71.25 cm and 41.25 cm

Let the initial lengths of the rods(at $0^{\circ }C$) be $l_1$ and $l_2$.

Since the difference in lengths at all temperatures is $30cm$,

$l_2-l_1=30$

and $l_1(1+{\alpha }_1\Delta \theta )-l_2(1+{\alpha }_2\Delta \theta )=30$

$⟹l_1{\alpha }_1=l_2{\alpha }_2$
$⟹11l_1=19l_2$

and $l_1-l_2=30cm$

$⟹l_1=71.25cm,l_2=41.25cm$