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?

7:5

5:7

1:2

2:1

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Som15432

1 year ago

The Core Idea
The question is about how much the lengths of two metal rods, P and Q, change when they are heated. This change in length depends on:
* Original Length: Longer rods tend to expand more.
* Linear Expansivity: This is a property of the material. Some materials expand more than others for the same temperature change.
* Temperature Change: The bigger the temperature change, the more the rods will expand.
Given Information
* Lengths: P has length L1, Q has length L2. The ratio L1:L2 is 3:4.
* Linear Expansivities: P has expansivity α1, Q has expansivity α2. The ratio α1:α2 is 2:3.
* Temperature Change: Both rods experience the same temperature change (let's call it ΔT).
What We Want to Find
We need to find the ratio of the increase in length of P (ΔL1) to the increase in length of Q (ΔL2), which is ΔL1:ΔL2.
The Formula
The change in length (ΔL) is given by:
ΔL = L * α * ΔT
Where:
* ΔL = change in length
* L = original length
* α = linear expansivity
* ΔT = change in temperature
Let's Solve It
* Change in Length for P (ΔL1):
ΔL1 = L1 * α1 * ΔT
* Change in Length for Q (ΔL2):
ΔL2 = L2 * α2 * ΔT
* Ratio of Increases (ΔL1:ΔL2):
(ΔL1 / ΔL2) = (L1 * α1 * ΔT) / (L2 * α2 * ΔT)
Notice that ΔT cancels out:
(ΔL1 / ΔL2) = (L1 * α1) / (L2 * α2)
* Substitute the Ratios:
We know L1:L2 = 3:4, so L1/L2 = 3/4
We know α1:α2 = 2:3, so α1/α2 = 2/3
Plug these in:
(ΔL1 / ΔL2) = (3/4) * (2/3)
* Simplify:
(ΔL1 / ΔL2) = (3 * 2) / (4 * 3) = 6/12 = 1/2
Answer
The ratio of the increase in length of P to Q is 1:2, which is option C.

Olawale4

9 years ago

The question is wrongly composed:

The answer is D. This is because;

Sickle Cell carrier: AS

Normal: AA

The crossing: AS AA

which gives the offsprings with: AA, AA, AS, AS

which means the offsprings are all NORMAL. Meanwhile, AS are also normal but only carrying the disease. So, the ratio is 4:4 which gives the answer to be 1 (D)

REF: Essential Biology