A metre scale made of steel reads accurately at 20°C. In a sensitive experiment, distances up to 0.055 mm in 1 m are required. Find the range of temperature in which the experiment can be performed with this metre scale. Coefficient of linear expansion of steel = 11 × 10^–6 °C^–1.

Question

Philoid · Accepted Answer

Given:

Temperature at which meter scale gives accurate reading: T₁=20° C

Change in Length required: Δ L=0.055mm = 0.055 x 10^-3 m.

Original Length: L= 1 m.

Coefficient of linear expansion of steel: α = 11 x 10^-6 ° C^-1.

Formula used:

Now, we have the direct formula for change in length due to thermal expansion:

Where Δ L is the change in length.

Where Δ T is the change in temperature,

it can be T₁+T₂ OR T₁-T₂.

First let’s take T₁-T_2.

Now, let’s take T₁+T_2,

Hence, the range of the temperature within which this experiment can be performed with the given metre scale is 15° C to 25° C.

A metre scale made of steel reads accurately at 20°C. In a sensitive experiment, distances up to 0.055 mm in 1 m are required. Find the range of temperature in which the experiment can be performed with this metre scale. Coefficient of linear expansion of steel = 11 × 10–6 °C–1.