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A student records the initial length l, change in temperature $\Delta T$ and change in length $\Delta l$ of a rod as follows:

S.No

l (m)

$\Delta T (^{\circ}C)$

$\Delta l (m)$

1

2

10

$4 \times 10^{-4}$

2

1

10

$4 \times 10^{-4}$

3

2

20

$2 \times 10^{-4}$

4

3

10

$6 \times 10^{-4}$

If the first observation is correct, what can you say about observations 2, 3, and 4.

Answers (1)

$\Delta t$ is same here.

Now, from observation no. 1

$\alpha =\frac{\Delta L}{L \Delta t}$

$\frac{4 \times 10^{-4}}{2 \times 10}= 2 \times 10^{-5} C^{\circ}-1$

Now, for observation no. 2,

$\Delta L=\alpha L \Delta t$

$= 2 \times 10^{-5} \times 1 \times 10$

$= 2 \times 10^{-4}m$ viz. not equal to $4 \times 10^{-4}m$

Now, for observation no. 3,

$\Delta L=\alpha L \Delta t$
$= 2 \times 10^{-5} \times 2 \times 20$

$= 8 \times 10^{-4}$ viz. not equal to $= 2 \times 10^{-4}m$

Now, for the last observation, i.e., no. 4,

$\Delta L=\alpha L \Delta t$

$= 2 \times 10^{-5} \times 3 \times 10$

$= 6 \times 10^{-4 }= 6 \times 10^{-4}m.$

Posted by

infoexpert24

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