Two metals P and Q of length l1 and l2 are heated through the same temperature difference. If the ratio of the linear expansivities of P to Q is 2:3 and the ratio of lengths is 3:4. What is the ratio of increase in length of P to Q?
A
7:5
B
5:7
C
1:2
D
2:1
Verified Correct Answer: C.
Physical Principles & Numerical Solution
Metals P, Q
original length lP, lQ
Increase in length \DeltalP, \DeltalQ
Linear expansivities \alphaP, \alphaQ
∴ \alphaP/\alphaQ = 2/3 ; and lP/lQ = 3/4
But increase in length, \Deltal = \alphal\Delta\theta
∴\DeltalP = \alphaPlP\Delta\theta
\DeltalQ = \alphaQlQ\Delta\theta
∴
\DeltalP
=
\alphaPlP\Delta\theta
=
2
x
3
=
1
\DeltalQ
\alphaQlQ\Delta\theta
3
4
2
∴ Ratio of increase in length of P to Q = 1:2
Source: WAEC / JAMB / NECO Classroom Archive (Record #14509)