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Question
A student records the initial length l, change in temperature ∆T and change in length ∆l of a rod as follows:
| S.No. | l(m) | ∆T (C) | ∆l (m) |
| 1. | 2 | 10 | `4 xx 10^-4` |
| 2. | 1 | 10 | `4 xx 10^-4` |
| 3. | 2 | 20 | `2 xx 10^-4` |
| 4. | 3 | 10 | `6 xx 10^-4` |
If the first observation is correct, what can you say about observations 2, 3 and 4.
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Solution
As per the 1st observation, we can infer that linear expansion α is,
α = `(∆l)/(l∆t)`
= `(4 xx 10^-4)/(2 xx 10)`
= `2 xx 10^(-5^circ) C^-1`
For observation no. 2,
α = `(∆l)/(l∆t)`
`∆l = αl∆t`
= `2 xx 10^-5 xx 1 xx 10`
= `2 xx 10^-4 m`
But given value is `∆l = 4 xx 10^-4 m`
So, 2nd observation is incorrect.
For observation no. 3,
α = `(∆l)/(l∆t)`
`∆l = αl∆t`
= `2 xx 10^-5 xx 2 xx 20`
= `8 xx 10^-4 m`
But the given value is `∆l = 2 xx 10^-4 m`
So, 3rd observation is incorrect.
For observation no. 4,
α = `(∆l)/(l∆t)`
`∆l = αl∆t`
= `2 xx 10^-5 xx 3 xx 10`
= `6 xx 10^-4 m`
Here the obtained value is the same as the given value.
So, the 4th observation is correct.
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