Question

If two physical quantites have the same dimensions, do they represent the same physical content

Answer 1

Answer:

No, if two physical quantity have same dimension they do not necessarily represent same physical quantity.

Explanation:

If two physical quantity have same dimension, its not always necessary that they represent the same quantity.

For example:

We know pressure is defined as force per unit area

$P=\frac{F}{A}$, it has the dimension $N/m^2$

At  the same time Young's modulus is defined by

$Y=\frac{stress}{strain}$, Stress has unit $N/m^2$ and strain is unitless quantity. Hence the unit of Young's modulus is $N/m^2$. But pressure and Young's modulus are two different quantity.

Another example is, work and energy they both have  same unit defined as Joule. But they are two different property of object.