question_answer 36)

                  A students records the initial length \[l\], change in temperature              \[\Delta T\] and change in length \[\Delta l\] of a road as follows :                

S. No.	\[l(m)\]	\[\Delta T{{(}^{o}}C)\]	\[\Delta l(m)\]
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 if correct, what can you say about observations 2, 3 and 4.                

Answer:

                  From first observation.                 \[\alpha =\,\frac{\Delta l}{l\Delta l}\,=\frac{4\times \,{{10}^{-4}}}{2\times 10}\,=2\,\times \,{{10}^{-5}}{{\,}^{o}}{{C}^{-1}}\]                 Ford 2nd observation, \[\Delta l=\,l\,\alpha \,\Delta T\]                 \[=1\times 2\times {{10}^{-5}}\,\times 10\]                 \[=2\times {{10}^{-4}}\,m\,(\ne 4\times {{10}^{-4}}\,m)\]                 Ford 3rd observation, \[\Delta l=\,l\,\alpha \,\Delta T\]                 \[=2\times 2\times {{10}^{-5}}\times 20\]                 \[=8\times {{10}^{-4}}m(\ne 2\times {{10}^{-4}}\,m)\]                 For 4th observation, \[\Delta l\,=l\,\alpha \,\Delta T\]                 \[=3\times 2\times {{10}^{-5}}\times 10\]                 \[=6\times {{10}^{-4}}\,m\]                 Thus observation 2 and 3 are incorrect and observation 4 is correct.