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A metallic tape gives the correct value at \[25^\circ C\]. A piece of wood is being measured by this metallic tape at \[10^\circ C\]. The reading is \[30cm\] on the tape, the real length of wooden piece must be:
A) \[30cm\]
B) \[ > 30cm\]
C) \[ < 30cm\]
D) Data is not sufficient

Last updated date: 20th Jun 2024
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Hint: We know metallic strips change its length as temperature changes depending upon linear expansion coefficient and if length L and if the temperature increases then length will increase otherwise it decreases by \[\Delta L\].

Complete step by step answer:
As in this given question we are given metallic tape and we know metallic tape changes its length when temperature around it changes but it all depends upon linear coefficient of length. As we know the formula
\[\Delta L = L\alpha \Delta T\], here \[L\],\[\alpha \] and \[\Delta T\] are length , linear coefficient constant and change in temperature respectively. So if it is showing the correct length at \[25^\circ C\] and at \[10^\circ C\] it is showing the length as \[30cm\],so if increase the temperature to \[25^\circ C\] the length will be more than \[30cm\] due to increase in length by increase in temperature and we can also solve it mathematically by using the formula of
\[\Delta L\] as \[\Delta L = L\alpha \Delta T\] and if we substitute the given values in question we will get the length coming approximately \[35cm\] that is greater than \[30cm\].

So the correct answer is B.

Note:There are various misconceptions of numerous students regarding such questions when the temperature change causes errors in the readings, especially for metallic tapes and scales. Many students believe that since the temperature is increasing, or decreasing, then, the lengths of both, the scale or tape and the object to be measured would increase or decrease respectively. But they forget to consider the fact that even if it happens, the linear coefficient constant would differ for both of the materials, the one using which scale or tape was manufactured and the one with which the object is prepared. Hence, proceed carefully with such questions if you don’t want to lose easy marks.