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.

Answer 1

As per the 1^st 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, 2^nd 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, 3^rd 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 4^th observation is correct.