Dimensions of Force Constant

Dimensional Formula of Energy Density

The dimensional formula of energy density is given by,

[M1 L0 T-2]

Where,

  • M = Mass
  • L = Length
  • T = Time

Derivation

Force Constant= Force × [Displacement]-1 . . . (1)

Since, Force = m × a

Therefore, the dimensions of force = [M1 L1 T-2] . . . (2)

And, the dimensional formula of displacement = [M0 L1 T0] . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Force Constant= Force × [Displacement]-1

= [M1 L1 T-2] × [M0 L1 T0]-1 = [M1 L0 T-2].

Therefore, the energy density is dimensionally represented as [M1 L0 T-2].

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