When a metal ball is heated through 30oC,its volume becomes 1.0018cm3. If the linear expansivity of the material of the ball is 2.0 x 10-5 K-1, calculate its original volume
A
1.0000cm3
B
1.0020cm3
C
1.0036cm3
D
1.0180cm3
Verified Correct Answer: A.
Physical Principles & Numerical Solution
\(\gamma\) = \(\frac{\delta\ V}{V_1\delta\theta}\)
but \(\gamma\) = 3\(\alpha\) and \(\delta\)V = \(V_2 - V_1\),
making \(V_1\) subject of formula we have
\(V_1 = \frac{V_2}{3\alpha\delta\theta + 1} = \frac{1.0018}{3 \times 2.0 \times 10^{-5} \times 30 + 1}\)
= 1\(cm^3\)
\(\therefore\) the original volume of the metal ball = 1.0000\(cm^3\)
Source: Myschool Past Questions Archive (Record #34320)