First slide

Thermal expansion

Question

A meter rod made of steel is correct at 0°C and other meter rod of same material is correct at 30°C. If α = 12 × 10^–6/°C, the difference between their lengths at 20°C is

Easy

A

0.024 cm
B

0.012 cm
C

0.036 cm
D

0.048 cm

Solution

For first rod, $\large l_2=l_1[1+\alpha. \Delta t_1]$
$\large =l_1[1+\alpha(20-0)]=l_1+l_1(20\alpha).....(1)$
For second rod, $\large {l}'_2=l_1[1+\alpha(20-30)]=l_1-l_1(10\alpha).....(2)$
$\large l_2-{l}'_2=30\alpha l_1=30(12\times 10^{-6})(100)$
$\large =36\times 10^{-3}\;cm$

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