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A student records the initial length l, ...

A student records the initial length l, change in temperature `Delta T` and change in length `Delta T` of a rod as follows
`{:("S.No.","l(m)",Delta T(.^(@)C),Delta l(m)),(1.,2,10,4xx 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 observation 2, 3 and 4.

Text Solution

Verified by Experts

From the 1st observation `alpha = (Delta l)/(l Delta l) rArr = (4 xx 10^(-4))/(2 xx 10) = 2 xx 10^(-5) .^(@)C^(-1)`
For 2nd obervation `Delta l = alpha l Delta T`
`= 2 xx 10^(-5) xx 1 xx 10 =2 xx 10^(-4)m != 4 xx 10^(-4)m` (Wrong)
For 3rd observation `Delta l =alpha l Delta T`
`= 2 xx 10^(-5) xx 2 xx 20 = 8 xx 10^(-4)m != 2 xx 10^(-4)m` (Wrong)
For 4th observation `Delta l = alpha l Delta T`
`= 2 xx 10^(-5) xx 3 xx 10 = 6 xx 10^(-4)m = 6 xx 10^(-4) m` [i.e., observed value (Correct)]
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