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A steel rular exactly 20 cm long is grad...

A steel rular exactly `20 cm` long is graduated to give correct measurements at `20^@C`.
(a) Will it give readings that are too long or too short at lower temperatures?
(b) What will be that actual length of the rular when it is used in the desert at a temperature of `40^@ C` ? `alpha_(steel) = 1.2 xx 10^-5(.^@ C)^-1` .

Text Solution

Verified by Experts

(a) If the temperature decreases, the length of the ruler also decreases through thermal contration. Below
`20^(@)C`, each centimeter division is actually somewhat shorter than 1.0 cm, so the steel ruler gives read-
ings that are too long.
(b) At ` 40^(@)C`, the increase in length of the ruler is
` Deltal = lalpha DeltaT = (20) (1.2xx10^(-5)) (40^(@)-20^(@))= 0.48 xx 10^(-2)cm`
`therefore` The actual length of the ruler is,`l^(1)= l + Deltal = 20.0048 cm`
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