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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 $\Delta L$.
$\Delta L = L\alpha \Delta T$, 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 $30cm$.