Q. 115.0( 1 Vote )

# 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.

0.99989cm

Explanation:

Given:

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

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

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

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