Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# A Metre Scale Made of Steel is Calibrated at 20°C to Give Correct Reading. - Physics

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

#### Solution

Given:
Temperature at which the steel metre scale is calibrated, t1 = 20oC
Temperature at which the scale is used, t2 = 10oC
So, the change in temperature,

$\Delta$t = 20o

$-$10o) C

The distance to be measured by the metre scale, Lo = 51

-50) = 1 cm = 0.01 m
Coefficient of linear expansion of steel,

$\alpha_{steel}$= 1.1 × 10–5 °C–1

Let the new length measured by the scale due to expansion of steel be L​2, Change in length is given by,

ΔL = L1steel Δt

⇒ΔL = 1 × 1.1 × 10^-5 × 10

$\Rightarrow ∆ L = 0 . 00011 cm$

As the temperature is decreasing, therefore length will decrease by

$∆ L$

Therefore, ​the new length measured by the scale due to expansion of steel (L2) will be,
L2 = 1 cm

$-$ 0.00011 cm = 0.99989 cm

Concept: Temperature and Heat
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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 1 Heat and Temperature
Q 11 | Page 13