Question

The dimension of the physical quantity of power is ____
1. M¹L²T^-2
2. M¹L²T^-3
3. M¹L³T^-2
4. M¹L³T^-3

Answer 1

Correct Answer - Option 2 : M¹L²T^-3

The correct answer is M1L2T-3

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].

• Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit, and a Dimension is a mathematical tool used for studying the nature of physical quantities. 
• The basic concept of dimension 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.