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 (aCu=1.7 × 10-5 K-1 and .aAl=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 (aCu=1.7 × 10-5 K-1 and .aAl=2.2 × 10-5 K-1) (A) 88 cm (B) 68 cm (C) 6.8 cm (D) 113.9cm

Tardigrade Admin · Accepted Answer

Δ l1=Δ l2 l1 propto1 Δ θ=l2 propto2 Δ θ 88 × 1.7 × 10-5=l2 × 2.2 × 10-5 Δ I2=88 × 1.7 / 2.2=68 cm

Q. A copper rod of $88 c m$ and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is $(a_{C_{u}} = 1.7 \times 1 0^{- 5} K^{- 1}$ and $a_{A_{l}} = 2.2 \times 1 0^{- 5} K^{- 1})$

88 cm

68 cm

6.8 cm

113.9cm

$Δ l_{1} = Δ l_{2}$
$l_{1} \propto_{1} Δ θ = l_{2} \propto_{2} Δ θ$
$88 \times 1.7 \times 1 0^{- 5} = l_{2} \times 2.2 \times 1 0^{- 5}$
$Δ I_{2} = 88 \times 1.7/2.2 = 68 c m$

Q. A copper rod of 88cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is (aCu​​=1.7×10−5K−1 and aAl​​=2.2×10−5K−1)