Question 358: Properties of Matter

Question

Coefficient of linear expansion of brass and steel rods are $\alpha $
1
and $\alpha $
2
. Lengths of brass and steel rods are $l$
1
and $l$
2
respectively. If ($l$
1
$-$ $l$
2
) is maintained same at all temperatures, which one of the following relations holds good?

Accepted Answer

From question, $\left( {{l_2} - {l_1}} \right)$ is maintained same at all temperatures hence change in length for both rods should be same
i.e., $\Delta {l_1} = \Delta {l_2}$
As we know, coefficient of linear expansion,
$\alpha  = {{\Delta l} \over {{l_0}\Delta T}}$
${l_1}{\alpha _1}\Delta T = {l_2}{\alpha _2}\Delta T$
${l_1}{\alpha _1} = {l_2}{\alpha _2}$

Answer

$\alpha $
1
$l$
2
= $\alpha $
2
2
$l$
1

Answer

$\alpha $
1
$l$
1
= $\alpha $
2
l
2

Answer

$\alpha $
1
$l$
2
= $\alpha $
2
$l$
1

Answer

$\alpha $
1
$l$
2
2
= $\alpha $
2
$l$
1
2

Properties of Matter

Coefficient of linear expansion of brass and steel rods are \alpha 1 and \alpha 2 . Lengths of brass and steel rods are l 1 and l 2 respectively. If (l 1 - l 2 ) is maintained same at all temperatures, which one of the following relations holds good?

Choose the correct answer: