A sphere-shaped casting solidifies on 10 min. What will be the so
| A sphere-shaped casting solidifies on 10 min. What will be the solidification time in minutes for another sphere of the same material, which is 8 times heavier than the original casting ?
A. 80
B. 10
C. 40
D. 20
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
Concept:
Solidification time(τ):
Solidification time for molten metal in mold is given by
τ = k1M2 , k1 = mold constant or solidification factor, M = Modulus
M= \(\frac{{Volume\;of\;casting}}{{Surface\;area}}\;\)
For sphere, M = \(\frac{D}{6}\)
\(∴ τ = {k_1}{\left( {\frac{D}{6}} \right)^2}\)
Calculation:
Given:
τ1 = 10 min, V2 = 8V1, τ2 =?
Now, we know that
V2 = 8V1 ⇒ (D2)3 = 8 (D1)3⇒ D2= 2D1
From the above equation,
\( τ = {k_1}{\left( {\frac{D}{6}\;} \right)^2}\)
\(\frac{{{τ _2}}}{{{τ _1}}} = {\left( {\frac{{{D_2}}}{{{D_1}}}} \right)^2}\)
\(\frac{{{τ _2}}}{{10}} = {\left( 2 \right)^2}\)
∴ τ2 = 40 min