Dimensions of Force

Dimensional Formula of Force

The dimensional formula of force is given by,

M1 L1 T-2

Where,

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

Derivation

Force = Mass × Acceleration . . . . (1)

Since, acceleration = velocity × [time]1 = [LT-1] × [T]-1

Therefore, the dimensional formula of acceleration = [LT-2] . . . . (2)

On substituting equation (2) in equation (1) we get,
Force = m × a
Or, F = [M] × [L1 T-2] = M1 L1 T-2.
Therefore, Force is dimensionally represented as M1 L1 T-2.

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