| A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is- [NEET 2019] |
| \[({{\alpha }_{Cu}}=1.7\times {{10}^{5}}\text{ }{{K}^{1}}\text{ }and\,{{\alpha }_{Al}}=\]\[~2.2\times {{10}^{5}}\text{ }{{K}^{1}})\] |
A) 88 cm
B) 68 cm
C) 6.8 cm
D) 113.9 cm
Correct Answer: B
Solution :
| [b] \[\Delta {{\ell }_{1}}=\Delta {{\ell }_{2}}\] |
| \[{{\ell }_{1}}{{\alpha }_{1}}={{\ell }_{2}}{{\alpha }_{2}}\] |
| \[\frac{{{\ell }_{1}}}{{{\ell }_{2}}}=\frac{{{\alpha }_{2}}}{{{\alpha }_{1}}}\] |
| \[\frac{88}{{{\ell }_{a}}}=\frac{2.2\times {{10}^{-5}}}{1.7\times {{10}^{-5}}}\] |
| \[{{\ell }_{a}}=68cm\] |
| Comment: In this question it should be difference in length instead of increase in length. |
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