A steel tape 1 m 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 10-1K-1.

As a seasoned tutor on UrbanPro, I can certainly help with this question, and I'm glad you're interested in learning. Let's break down the problem step by step:

First, we'll find the increase in length of the steel tape due to the rise in temperature from 27.0°C to 45.0°C. We'll use the formula for linear expansion:

ΔL=L⋅α⋅ΔTΔL=L⋅α⋅ΔT

Where:

• ΔLΔL is the change in length
• LL is the original length of the steel tape
• αα is the coefficient of linear expansion of steel
• ΔTΔT is the change in temperature

Given that L=1L=1 meter, α=1.20×10−5 K−1α=1.20×10−5K−1, and ΔT=45.0°C−27.0°C=18.0°CΔT=45.0°C−27.0°C=18.0°C, we can calculate:

ΔL=(1.0 m)×(1.20×10−5 K−1)×(18.0°C)ΔL=(1.0m)×(1.20×10−5K−1)×(18.0°C)

ΔL=0.000216 m=0.216 cmΔL=0.000216m=0.216cm

So, the increase in length of the steel tape is 0.216 cm.

Now, let's find the length of the steel rod on the hot day (45.0°C):

Given length measured by the tape = 63.0 cm Increase in length of the tape = 0.216 cm

Therefore, the actual length of the steel rod on that day is:

Actual length=Measured length−Increase in length of tapeActual length=Measured length−Increase in length of tape

Actual length=63.0 cm−0.216 cm=62.784 cmActual length=63.0cm−0.216cm=62.784cm

So, the actual length of the steel rod on the hot day is 62.784 cm.

Now, for the length of the same steel rod on a day when the temperature is 27.0°C, there is no change in temperature from the calibration temperature of the tape. Therefore, the length measured by the tape will be the actual length of the steel rod, which is 63.0 cm.

In summary:

• Actual length of the steel rod on the hot day (45.0°C): 62.784 cm
• Length of the steel rod on a day when the temperature is 27.0°C: 63.0 cm

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