Question

If the coefficient of real expansion, ${\gamma }_r$ is 1% more than coefficient of apparent expansion, linear expansion coefficient of the material is :

• A. $\frac{{\gamma }_r}{303}$
• B. $\frac{100{\gamma }_r}{101}$
• C. $\frac{101{\gamma }_r}{300}$
• D. $\frac{101{\gamma }_r}{100}$

Answer 1

The correct option is A $\frac{{\gamma }_r}{303}$

${\gamma }_r=1.01\ast {\gamma }_a$ as given
${\gamma }_r={\gamma }_a+{\gamma }_g={\gamma }_a+3{\alpha }_g$
$\therefore 1.01\ast {\gamma }_a={\gamma }_a+3{\alpha }_g$
$\therefore 0.01\ast {\gamma }_r\ast \frac{1}{1.01\ast 3}={\alpha }_g$
$\therefore {\alpha }_g=\frac{{\gamma }_r}{303}$