Question

An iron rod of length 50 cm is joined at an end
to an aluminium rod of length 100 cm. All
measurements refer to 20°C. The coefficients
of linear expansion of iron and aluminium are
12 x 10*-6/°C and 24 x 10*-6/°C respectively. The
average linear expansion coefficient of
composite system is :-​

Answer 1

The  average linear expansion coefficient of  composite system is 3 ×10⁻³ cm/C.

The average linear expansion coefficient of two systems are given as

I₁ + I₂, where I₁ and I₂ are the linear expansion of each system.

and I = length × coefficient of linear expansion

For Iron,

length = 50cm

coefficient of linear expansion = 12×10⁻⁶ /C

So, I₁ =  50 × 12×10⁻⁶ = 6×10⁻⁴ cm/C

For Aluminium,

length = 100cm

coefficient of linear expansion = 24×10⁻⁶ /C

So, I₂=  100 × 24×10⁻⁶ = 24×10⁻⁴ cm/C

So, total linear expansion coefficient of the system is

I₁ + I₂ = (6×10⁻⁴ + 24×10⁻⁴) cm/C = 30 ×10⁻⁴ cm/C

= 3 ×10⁻³ cm/C