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

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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