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 [2019]

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Solution

Q.
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 $(α_{Cu} = 1.7 \times 10^{- 5} K^{- 1}, α_{Al} = 2.2 \times 10^{- 5} K^{- 1})$ [2019]

1 68 cm

2 6.8 cm

3 113.9 cm

4 88 cm

Ans.
(1)

As per question, $Δ l_{Cu} = Δ l_{Al}$

or, $l_{Cu} α_{Cu} Δ T = l_{Al} α_{Al} Δ T$

$l_{Al} = \frac{l_{Cu} α_{Cu}}{α_{Al}} = \frac{88 \times 1.7 \times 10^{- 5}}{2.2 \times 10^{- 5}} = 68$ $cm$

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