Question

The coefficient of linear expansion of brass is $2\times {10}^{-5}{C}^{-1}$. Find its (i) coefficient of superficial expansion, (ii) coefficient of cubical expansion.

Let $xandy$ be the answers write $(y-x)\times {10}^5$

Answer 1

Coefficient of linear expansion = $\alpha$ = $2\times {10}^{-5}{C}^{-1}$

Coefficient of superficial expansion = $\beta$ = $2\alpha$

$\therefore \beta =2\times (2\times {10}^{-5})=4\times {10}^{-5}$

Coefficient of cubical expansion =

$\gamma =3\alpha =3\times (2\times {10}^{-5})=6\times {10}^{-5}$

Let the coefficient of cubical expansion and coeficient of superficial expansion be $y$ and $x$ respectively.

$\therefore (y-x)\times {10}^5=(6\times {10}^{-5}-4\times {10}^{-5})\times {10}^5=(6-4)\times {10}^{-5}\times {10}^5=2$