If velocity, time and force were chosen as basic quantities, find the dimensions of mass and energy.

The Dimension of mass is [F T v⁻¹] and Dimension of energy is [F T v]

Explanation:

(i) We know that,

Force = mass × acceleration

= mass × velocity/time

⇒ mass = force × time ÷ velocity

or. [mass] = [force] [time] ÷ [velocity]

= [F] [T] ÷ [v]

∴ [mass] = [F T v⁻¹]

(ii) Dimensions of energy are same as the dimensions of kinetic energy

∴ Energy = [ ½mv²] = [m] [v]²

= [F T v⁻¹] [v]²

Energy = [F T v]

Thus, The Dimension of mass is [F T v⁻¹] and Dimension of energy is [F T v]

-TheUnknownScientist

frequency or wavelenth of em radiation in a vacuum