A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temprature . The length  of aluminium rod is : 

(^\alpha C_u = 1.7 \times 10 ^{-5} K^{-1} \: \: and \: \: ^ \alpha A1 = 2.2 \times 10 ^{-5}K^{-1})

  • Option 1)

    6.8 cm 

  • Option 2)

    113.9 cm 

  • Option 3)

    88 cm 

  • Option 4)

    68 cm 

 

Answers (1)
V Vakul

For Copper \rightarrow L = 88 cm 

\Delta L = L_ 0 \alpha \Delta T

 \Delta L \: \: to \: \: independent\: \: of \: \: \Delta T \\\\ \frac{\Delta L}{\Delta T} = L_0 \alpha = const\\\\ \left ( L_0 \alpha \right )_{Cu} = (L \alpha )_{AI}\\\\ (1.7 \times 10 ^{-5})\times 88 = ( 2.2 \times 10 ^{-5})\times L_ {Al} \\\\ L_{Al} = \frac{1.7 \times 4}{10 ^{-1}} \\\\ = 68 cm


Option 1)

6.8 cm 

Option 2)

113.9 cm 

Option 3)

88 cm 

Option 4)

68 cm 

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