Question

Ratio of solidification time of cylindrical casting (height = radius) to that of a spherical casting of radius two times the radius of cylindrical casting is _______ . (Upto two decimal places)

• A. 1
• B. 0
• C. 0.14
• D. 0.5

Answer 1

The correct option is C 0.14


Modulus of casting 1,

$m_1=\frac{\pi r^{2}h}{2\pi rh+2\pi r^2}=\frac{\pi r^3}{4\pi r^2}=\frac{r}{4}$

Modulus of casting 2,

$m_2=\frac{\frac{4}{3}\pi (2r{)}^3}{4\pi (2r{)}^2}=\frac{2r}{3}$

$\frac{{\tau }_1}{{\tau }_2}={\left(\frac{m_1}{m_2}\right)}^2={(\frac{r}{4\times 2r}\times 3)}^2={\left(\frac{3}{8}\right)}^2=0.14$