A steel rular exactly 20 cm long is graguated 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 .
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Explanation:
a) If the temperature decreases, the length of the rular also decreases through thermal contraction. Below 20∘C, each centimetre division is actually somewhat shorter than 1.0cm, so the steel ruler gives readings that are too long.
(b) At 40∘C, the increase in length of the ruler is
Δl = (l α Δ T)
= 20 x 1.2 x 10^-5 ( 40° - 20°)
= 0.48 x 10 ^ -2 cm
The actual length of the ruler is
l = l + Δl
20.0048 cm
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