Question

why we are writing F/1 N = ∆l/∆l0 in place of 1 N proportional to ∆l0? We use constant when we remove proportional symbol. please help​

Answer 1

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What is Constant of Proportionality?

• Constant of proportionality is the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of proportionality when, either their ratio or their product yields a constant. The value of the constant of proportionality depends on the type of proportion between the two given quantities: Direct Variation and Inverse Variation.

Direct Variation : The equation for direct proportionality is y = kx, which shows as x increases, y also increases at the same rate. Example: The cost per item(y) is directly proportional to the number of items(x) purchased, expressed as y ∝ x

Inverse Variation : The equation for the indirect proportionality is y = k/x, which shows that as y increases, x decreases and vice-versa. Example:The speed of a moving vehicle (y) inversely varies as the time taken (x) to cover a certain distance, expressed as y ∝ 1/x

In both the cases, k is constant. The value of this constant is called the coefficient of proportionality. The constant of proportionality is also known as unit rate.

constant of proportionality in direct and inverse variation

Why Do We Use The Constant of Proportionality?

We use constant of proportionality in mathematics to calculate the rate of change and at the same time determine if it is direct variation or inverse variation that we are dealing with. Let us assume that the cost of 2 apples = $20.

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Answer 2

Answer:

When we mean proportionality or inverse proportionality we imply just what the words imply, that the value in consideration changes with respect to how dependent it is on the change in the other object.

For example, Newton found out that gravity is inversely proportional to the square of the point from the origin of gravitational force. So, F α1r2 .

He also assumed that product of main and secondary object was the cause of gravitational force. So, Fαm1m2

Taking these together, he assumed that Fαm1m2r2 .

G was that constant that he threw in just to remove the proportionality.