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 :
(ᵅcᵤ = 1.7 × 10⁻⁵ K⁻¹ तथा ᵅΑl = 2.2 × 10⁻⁵ K⁻¹)
(1) 6.8 cm
(2) 113.9 cm
(3) 88 cm
(4) 68 cm

Answer 1

The length of aluminium rod is 68 cm.

Step by step explanation:

Length of copper = $L_{cu}$ = 88 cm

Length of aluminium = $L_{Al}$ = ?

From the given,

$\alpha _{Cu}=1.6\times 10^{-5}$

$\alpha _{Al}=2.2\times 10^{-5}$

From the given condition-, Increase in length independent of increase in temperature.

The length of aluminium rod is calculated by the following formula.

$\bold{\alpha _{Cu}L_{Cu}=\alpha _{Al}L_{Al}}$.....................(1)

Substitute the given values in equation (1)

$1.7\times 10^{-5}\times 88=2.2\times 10^{-5}\times L_{Al}$

                         $\Rightarrow L_{Al}=\frac{1.7\times 88}{2.2}=68cm$

Therefore, The length of aluminium rod is 68 cm.