A metal rod has a length of 100cm at 200°C. At what temperature will its length be 99.4cm. If the linear expansivity of the material of the rod is 2 × 10\(^{-5}\)C\(^{-1}\)
A
\(300^0C\)
B
\(200^0C\)
C
\(100^0C\)
D
\(-100^0C\)
Verified Correct Answer: D.
Physical Principles & Numerical Solution
L\(_1\) = 100cm, T\(_1\) = 200^\circC
L\(_2\) = 99.4cm, T\(_2\) = ?
\alpha 2 \times 10\(^{-5}\) C\(^{-1}\)
\alpha
=
L\(_2\) - L\(_1\)
L\(_1\)(T\(_2\) - T\(_1\))
2
\times
10\(^{-5}\)
=
110 - 99.4
100(200 - T\(_2\))
=
0.6
100(200 - T\(_2\))
2 \times 10\(^{-5} \times 100(200 - T_2\)) = 0.6
200
-
T\(_2\)
=
0.6
0.002
=
300^\circC
T\(_2\) = 200 - 300 = -100^\circC
Source: WAEC / JAMB / NECO Classroom Archive (Record #55260)