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.

⇒ Check Other Dimensional Formulas:

• Dimensions of Angular Speed
• Dimensions of Strain
• Dimensions of Modulus of Rigidity
• Dimensions of Reynolds Number
• Dimensions of Universal Gas Constant

Internal and External Forces