Question 334: 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 = $$\alpha $$2l2

Answer

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

Answer

$$\alpha $$1$$l$$22  = $$\alpha $$2$$l$$12

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 l1 and l2 respectively. If (l1 - l$2) is maintained same at all temperatures, which one of the following relations holds good?

Choose the correct answer: