A metal sheet of area 100cm\(^2\) was heated through 70^\circC. Calculate its new area if the linear expansivity of the metal is 0.000017K\(^{-1}\).
A
100.06 cm2
B
100.12cm2
C
100.24cm2
D
100.36cm2
Verified Correct Answer: C.
Physical Principles & Numerical Solution
Formula: A\(_2\) = A\(_1\)(1 + \(\beta \theta\))
where \(\beta\) = The area expansivity
\(\theta\) = Change in temperature.
\(\beta\) = 2\(\alpha\)
where \(\alpha\) = linear expansivity of the body.
⇒ \(\beta\) = 2 x 0.000017
= 0.000034 K\(^{-1}\)
\(\therefore\) A\(_2\) = 100 (1 + (0.000034 x 70))
= 100(1 + 0.00238)
= 100(1.00238)
= 100.238 cm\(^2\)
= 100.24 cm\(^2\) (to 2 d.p)
Source: Myschool Past Questions Archive (Record #35565)