Question

A steel rod of length \[0.5km\] is used in the construction of a bridge. It has to withstand a temperature change of \[{40^o}C\]. The gap that is allowed for its expansion is:
(\[\alpha = {10^{ - 6}}{/^o}C\])
A) 0.02cm
B) 0.02mm
C) 2m
D) 20mm

Answer 1

Hint: According to question we can say that they are asking the expansion in a metal rod due increase in temperature. So you find it with the help of formulas for finding change in length when change in temperature, length and coefficient of linear expansion is given. Such that you can calculate the new length of rod.

Complete step by step answer:
Formula for change in length with change in temperature:
\[\Delta L\; = \;\alpha L\Delta T\]
Where:
\[\Delta L = \] is change in length
\[\alpha = \] coefficient of linear expansion of the material
\[l = \] original length of rod
\[\Delta T = \] change in temperature
Now putting given values in the above equation:
\[\Delta L = {10^{ - 6}} \times 500 \times 40\]
\[\Delta L = {10^{ - 6}} \times 20000\]
\[\Delta L = \dfrac{{20000}}{{1000000}}\]
\[\Delta L = 0.02m\]
\[\Delta L = 2cm = 20mm\]
Hence, option D is correct.

Note: Whenever there is a rise in temperature of the body the kinetic energy of individual atoms increases. As in solid state atoms are packed together so they push their neighbouring atoms and thus it results in slight expansion of the object. For most substances under ordinary conditions, there is no preferred direction, and an increase in temperature will increase the solid’s size by a certain fraction in each dimension.