$($a$)$ The $$lead$$ in pencils is a graphite composition with a Young$$s modulus of about $1$X$10^9$ N$/$m$2.$ Calculate the change in length of the lead in an automatic pencil if you tap it straight into the pencil with a force of $4\mathrm{.}0$ N$.$ The lead is $0\mathrm{.}50$ mm in diameter and $60$ mm long. $($b$)$ Is the answer reasonable? That is$,$ does it seem to be consistent with what you have observed when using pencils?