Question

The scale on a steel mater stick calibrated at ${15^ \circ }C$ . What is the error in the reading of 60 cm at ${27^ \circ }C$ ? ${\alpha _{steel}} = 1.2 \times {10^{ - 5}}{{(^ \circ }C)^{ - 1}}$ .

Answer 1

According to question, we need to find the error in the reading of 60 cm at ${27^ \circ }C$ when the scale on a steel mater stick calibrated at ${15^ \circ }C$ . Now the formula to be used to solve this equation will be $\Delta l$ = (scale reading) $(\alpha )(\Delta T)$ .

Complete Step By Step Answer:
An error is defined as the difference between the actual or true value and the measured value. An error should not be confused with a mistake, the mistake can be avoided, while the error cannot be avoided but they can be reduced (minimized). Sequentially, to understand the concept of errors in measurement, we should know the two terms that define the error. They are true value and measured value. The true value is impossible to find by experimental means. It may be defined as the average value of an infinite number of measured values. The measured value is a single measurement of the object with the aim of being as accurate as possible.
There are three types of errors that are classified on the basis of the source they arise from;
a) Constant error: Constant error is described as the error that causes measurements to consistently deviate from their true value.
b) Systematic error: Systematic errors are errors which occur due to some known causes while taking measurements.
c) Random error: Random error depends on the capabilities of the observer. This error is caused by carelessness of the observer while taking measurements.
Now, the error in the reading will be
$\Delta l$ = (scale reading) $(\alpha )(\Delta T)$ .
= $(60)(1.2 \times {10^{ - 5}})({27^ \circ } - {15^ \circ })$
= $(60)(1.2 \times {10^{ - 5}})({12^ \circ })$
On further solving, we get,
= $0.00864cm$
So, the final answer is $0.00864cm$ .

Note:
Random errors are caused by sudden changes in experimental conditions. They are random and often unavoidable. Random errors may be unavoidable, but they can be minimized by taking multiple readings and averaging the results. Further, proper care of the equipment used also helps to avoid errors.