A metre scale made of steel is calibrated at 20°C to give a correct reading. Find the distance between 50 cm mark and 51 cm mark if the scale is used at 10°C. Coefficient of linear expansion of steel is 1.1 × 10^-5^oC^-1.

Question

Philoid · Accepted Answer

0.99989cm

Explanation:

Given:

The temperature at which the steel meter is calibrated, t₁ is 20^oC

The temperature at which the scale is used, t₂ is 10^oC

The linear expansion coefficient of the scale is 1.1 × 10^-5^oC^-1.

Formula used:

The relation connecting the length at a specified temperature () and that of with a standardized temperature can be written as,

Where,

L₀= Length at a reference temperature,

α= coefficient of linear expansion,

θ= Change in temperature.

Here, 20°C can be taken as reference temperature and hence, ₀=length between adjacent centimeter markings1cmm

α=1.1× 10^-5°C^-1,

θ= -10° C

Hence,

=0.0099989m

=0.99989cm(Ans.)

The final length between 50cm and 51cm marks will be 0.99989cm

A metre scale made of steel is calibrated at 20°C to give a correct reading. Find the distance between 50 cm mark and 51 cm mark if the scale is used at 10°C. Coefficient of linear expansion of steel is 1.1 × 10-5oC-1.