What is the dimensional formula of Power?

Question

Question

Answer 1

Concept:

Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit and Dimension is a mathematical tool used for studying the nature of physical quantities.
The basic concept of dimensions is that we can add or subtract only those quantities which have the same dimensions.
And the dimensional formula is defined as the expression of the physical quantity in terms of mass, length, and time.

Explanation:

Power – It is defined as the rate of doing work.

\(\therefore P = \frac{W}{t}\)

Where, P = power, W = work done and t = time.

Now,

As Work done = Force × Distance

Force = mass × acceleration

∴ Dimensional formula of force (F) = [M] × [LT^-2] = [MLT^-2]

Dimensional formula of work (W) = [ML²T^-2]

Dimensional formula of time (t) = [T¹]

\(P = \frac{{M{L^2}{T^{ - 2}}}}{{{T^1}}} = \frac{{M{L^2}}}{{{T^3}}}\)

∴ The dimensional formula of power P is [ML²T^-3].

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