Physics 2012 JAMB Past Questions - Question 20: Two metals P and Q are heated through the same temperature difference .If the ratio of the linear expansitives of P to Q is 2:3 and the ratio of their length is 3:4 respectively ,the ratio of the increase in length of P to Q is

Correct Answer

A

Explanation

To find the ratio of the increase in length of metals P and Q, we can use the formula for linear expansion:

ΔL = α * L * ΔT

Where:
ΔL is the change in length,
α is the linear expansivity,
L is the original length, and
ΔT is the change in temperature.

Let's assume that the change in temperature (ΔT) is the same for both metals P and Q.

Given that the ratio of the linear expansivities of P to Q is 2:3, we can assign values to them as follows:
Let the linear expansivity of P be 2x, and the linear expansivity of Q be 3x.

Given that the ratio of their lengths is 3:4, we can assign values to them as follows:
Let the length of P be 3y, and the length of Q be 4y.

Now, let's calculate the change in length for each metal:

For metal P:
ΔL_P = (2x) * (3y) * ΔT = 6xyΔT

For metal Q:
ΔL_Q = (3x) * (4y) * ΔT = 12xyΔT

Therefore, the ratio of the increase in length of P to Q is:
ΔL_P : ΔL_Q = 6xyΔT : 12xyΔT = 1:2

So, the ratio of the increase in length of P to Q is 1:2.