Question

A cube-shaped casting solidifies in 5 min. The solidification time in min for a cube of the same material, which is 8 times heavier than the original casting, will be

• A. 10
• B. 20
• C. 40
• D. 24

Answer 1

The correct option is B 20

$\text{Solidification time,}$

$t=k{\left(\frac{V}{A}\right)}^2$

$\text{For cube:}$

$\left(\frac{V}{A}\right)=\frac{a}{6}$

$\frac{t_1}{t_2}=\frac{a_1^2}{a_2^2}$

$t_2=5{\left(\frac{a_2}{a_1}\right)}^2.....\left(i\right)$

$m_1=V_1\times {\rho }_1$

$m_2=V_2\times {\rho }_2$

$V_2=8V_1$

$a_2^3=8a_1^3$

$\Rightarrow a_2=2a_1$

$\frac{a_2}{a_1}=2......\left(ii\right)$

$\text{From the Equations (i) and (ii)}$

$t_2=5{\left(2\right)}^2=5\times 4=20min$