PHYSICS

JAMB 2010 - Question 16

Physics 2010 JAMB Past Questions - Question 16: Two metals P and Q of lengths are heated through the same temperature difference. if the ratio of linear expansivities of P to Q is 2:3 and the ratio of their lengths is 3:4. What is the ratio of increase in lengths of P to Q?

Choose the correct answers from the options given.
Two metals P and Q of lengths are heated through the same temperature difference. if the ratio of linear expansivities of P to Q is 2:3 and the ratio of their lengths is 3:4. What is the ratio of increase in lengths of P to Q?
A:
B:
C:
D:
Examkits App

Examkit's JAMB CBT App

Practice JAMB offline with our Online, PC and Mobile App

  • ✅ 25+ years of past questions (2000 to 2025)
  • ✅ Video solutions and explanation to questions
  • ✅ E-library
  • ✅ Study by topic
  • ✅ And more.

Correct Answer

C

Explanation

The increase in length of a material due to heating can be calculated using the formula:

ΔL = α * L * ΔT

Where:
ΔL = Change in length
α = Linear expansivity
L = Original length
ΔT = Change in temperature

Let's assume that the increase in length for metal P is ΔLP, and the increase in length for metal Q is ΔLQ.

Given that the ratio of linear expansivities of P to Q is 2:3, we can write:

αP/αQ = 2/3

Given that the ratio of their lengths is 3:4, we can write:

LP/LQ = 3/4

We want to find the ratio of ΔLP to ΔLQ.

We can rearrange the linear expansivity ratio equation to express αP in terms of αQ:

αP = (2/3)αQ

Now, let's calculate the ratio of ΔLP to ΔLQ:

(ΔLP/ΔLQ) = (αP * LP * ΔT) / (αQ * LQ * ΔT)

Since ΔT is the same for both metals (heated through the same temperature difference), it cancels out:

(ΔLP/ΔLQ) = (αP * LP) / (αQ * LQ)

Substitute the expression for αP from the linear expansivity ratio equation:

(ΔLP/ΔLQ) = ((2/3)αQ * LP) / (αQ * LQ)

Now, simplify:

(ΔLP/ΔLQ) = (2/3) * (LP/LQ)

We know that LP/LQ = 3/4, so:

(ΔLP/ΔLQ) = (2/3) * (3/4)

Now, calculate the ratio:

(ΔLP/ΔLQ) = (2/3) * (3/4) = 2/4 = 1/2

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

Frequently Asked Questions

Examkits is a JAMB CBT practice platform that provides over 20 years of past questions, Post UTME questions, and detailed video solutions to help students prepare for their exams.

You can practice JAMB past questions online, on Android, or on a desktop using the Examkits app. Just register on our website and choose your preferred device.

Yes. Our Android and Windows versions support offline usage. Once downloaded and activated, no internet is required to use most of the features.

Yes, Examkits provides detailed video explanations for all JAMB past questions from 2000 to 2024, helping students understand how to solve each problem.

Examkits offers free practice for some subjects. However, full access requires a one-time affordable activation fee for each version of the app.