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 $$($$αCu $$=$$ $$1.7$$×$$10-5K-1$$ and α$$AI=$$ $$2.2$$ ×$$10-5$$ $$K-1)$$

Question

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 $$($$αCu $$=$$ $$1.7$$×$$10-5K-1$$ and α$$AI=$$ $$2.2$$ ×$$10-5$$ $$K-1)$$

Infinity Learn · Accepted Answer

ICut $$=$$ $$lcu(1+$$αCu∆$$T)--------(i)lAI$$' $$=$$ $$IAl(1+$$αAl∆$$T)$$ $$-----(ii)Equation$$ (ii)-Eq$$. $$(i)lAl$$' $$=$$ ICu' $$=$$ $$lAl+lAI$$αAl∆$$T-(lCu+lCu$$αCu∆$$T)lAl$$' $$-$$ lCu' $$=$$ lAl $$-$$ $$lCu+(lAl$$α$$Al-lCu$$α$$Cu)∆TThe increase in length is not depend on temperature.αCulCu $$=$$ α$$AllAl1.7$$ × $$10-5$$×$$88$$ $$=$$ $$2.2$$×$$10-5$$×lAllAl $$=$$ $$68cm$$

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 ( $α_{Cu} = 1.7 \times 10^{- 5} K^{- 1} and α_{AI} = 2.2 \times 10^{- 5} K^{- 1}$ )

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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 (αCu = 1.7×10-5K-1 and αAI= 2.2 ×10-5 K-1)

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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 ( $α_{Cu} = 1.7 \times 10^{- 5} K^{- 1} and α_{AI} = 2.2 \times 10^{- 5} K^{- 1}$ )