Question 7: If two quantities have different dimensions, is it possible to multiply and/or divide? Can we add or subtract them?

Answer

We can multiply or divide quantities having different dimensions, however, we cannot do this in case of addition and subtraction.
Take a simple example of momentum. Momentum is mass time velocity. Both mass and velocity have different dimensions; [M] and [LT^{-1}], respectively. However, they are multiplied to get momentum (quantity of motion) of that body.
The dimensions of momentum are [MLT^{-1}].
On the other hand, quantities of different dimensions cannot be added or subtracted. As an example, we cannot subtract time from mass, or add length of the road with the temperature of the surrounding.

(Have you ever seen dimensions of a derived quantity in terms of dimensions of the base quantities added or subtracted!)?

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Thanks. Very useful 🙂

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