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: