A metre scale made up of aluminium (αa = 24 × 10-6/°C) measures

1.	A metre scale made up of aluminium (αa = 24 × 10-6/°C) measures length of a steel rod (αs = 12 × 10-6/°C) at room temperature as 50.00 cm. Now the temperature of the room is increased by 100 °C. What can be said about the measured length of the rod at new temperature?
Answer» At new temperature T °C, change in length of rod is, ∆L_S = L₀(α_S∆T) = 50.00(12 × 10^-6 × 100) = 0.06 cm. Hence, the actual length of rod at T °C, L_S = 50.06 cm Due to change in temperature, along with rod, the scale will also increase in length. For aluminium, at T °C, ∆L_a = L₀(α_a∆t) = 100.00 × 24 × 10^-6 × 100 = 0.24 cm ∴ Length of the scale will be, L_a = 100.24 cm As, the expansion in scale is more than that in rod, the reading recorded by the scale at t°C will be less than 50 cm.

A metre scale made up of aluminium (αa = 24 × 10-6/°C) measures length of a steel rod (αs = 12 × 10-6/°C) at room temperature as 50.00 cm. Now the temperature of the room is increased by 100 °C. What can be said about the measured length of the rod at new temperature?

Answer»

At new temperature T °C,

change in length of rod is,

∆L_S = L₀(α_S∆T) = 50.00(12 × 10^-6 × 100)

= 0.06 cm.

Hence, the actual length of rod at T °C,

L_S = 50.06 cm

Due to change in temperature, along with rod, the scale will also increase in length.

For aluminium, at T °C,

∆L_a = L₀(α_a∆t) = 100.00 × 24 × 10^-6 × 100

= 0.24 cm

∴ Length of the scale will be,

L_a = 100.24 cm

As, the expansion in scale is more than that in rod, the reading recorded by the scale at t°C will be less than 50 cm.