Question

A circular hole of diameter $2.00cm$ is made in an aluminium plate at $0^{o}C$. What will be the diameter at ${100}^{o}C$ ? $\alpha$ for aluminum $=2.3\times {10}^{-5}{}^o{C}^{-1}$.

Answer 1

Given data,

$d_1=2cm=2\times {10}^{-2}$

$t_1=0^{o}C,t_2={100}^{o}C$

${\alpha }_{al}=2.3\times {10}^{-5}{/}^{o}C$

$d_2=d_1(1+\alpha \Delta t)=2\times {10}^{-2}(1+2.3\times {10}^{-5}{10}^2)$

$=0.02+0.000046=0.020046m=2.0046cm$