Question

Two cubical castings of the same metal and sizes of 2 cm side and 4 cm side are moulded in green sand. If the smaller casting solidifies in 2 mins, the expected time of solidifications of large casting will be

• A. 8 min
• B. 4 min
• C. 16 min
• D. $2\sqrt{8}min$

Answer 1

The correct option is A 8 min

$\text{Modulus}=\frac{V}{A}$

$\text{For cube 1,}{M}_1=\frac{2^3}{6\times 2^2}=\frac{8}{24}=\frac{1}{3}$

$\text{For cube 2,}{M}_2=\frac{4^3}{6\times 4^2}=\frac{64}{96}=\frac{2}{3}$

$\text{Solidification time}\propto {\left(\frac{V}{A}\right)}^2$

$t_s\propto M^2$

$\text{Hence, we have}$

$\frac{T_1}{T_2}=\frac{M_1^2}{M_2^2}$

$\text{Given data:}$

$T_1=2min$

$\Rightarrow T_2=2\times {\left(\frac{2}{3}\right)}^2\times {\left(\frac{3}{1}\right)}^2=8min$