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

Answer:

Assume that the first observation is right, which indicates that the linear expansion coefficient is as follows:

$ \alpha =\frac{\Delta l}{l\times \Delta T}=\frac{4\times {{10}^{-4}}}{2\times 10} $

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

For second observation,

$ \Delta l=\alpha l\Delta T=2\times {{10}^{-4}}m\ne 4\times {{10}^{-4}}m $

which is incorrect. For third observation, we have –

$ \Delta l=\alpha l\Delta T=8\times {{10}^{-4}}m\ne 2\times {{10}^{-4}}m $

Which is incorrect. Now, for fourth observation, we have –

$ \Delta l=\alpha l\Delta T=6\times {{10}^{-4}}m=6\times {{10}^{-4}}m $

which is correct.