Question

11
A steel tape 1m long is correctly calibrated for a temperature of 27.0 °C. The
length of a steel rod measured by this tape is found to be 63.0 cm on a hot day
when the temperature is 45.0 °C. What is the actual length of the steel rod on that
day? What is the length of the same steel rod on a day when the temperature is
27.0°C ? Coefficient of linear expansion of steel = 1.20 x 10-5 K-1
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Answer 1

Answer:

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Answer 2

Answer:

• The actual length of the rod at $45.0</li><li>^{\circ}C$ is $\rm{63.0136 \:cm.}$ It's length at $27.0^{\circ} C$is $\rm{63.0 \:cm}$

Explanation:

• Length of the steel tape at temperature T = 27°C, l = 1 m (100 cm)
• At temperature $T_{1} = 45°C$, the length of the steel rod, $l_{1}$ = 63 cm
• The Coefficient of linear expansion of steel, α = 1.20 × 10$^{-5}$K$^{-1}$
• Let $l_{2}$ be the actual length of the steel rod and l′ be the length of the steel tape at
• 45°C.

Length of the steel rod measured by the steel tape at 45°C can

be calculated as:

$l' = l + \alpha l (T_{1}-T)$

$\therefore\: l' = 100 + 1.20 \times 10^{-5} \times 100(45-27)$

$= 100.0216\: cm$

$l_{2} = \dfrac{100.0216}{100}\times 63$

$= 63.0136\: cm$

Hence,

The actual length of the rod at $45.0</p><p>^{\circ}C$ is $\rm{63.0136 \:cm}.$ It's length at $27.0^{\circ} C$is $\rm{63.0 \:cm.}$