What is the Dimensional Formula of Work and its Derivation?

Dimensional Formula of Work

The dimensional formula of Work is given by,

[M¹ L² T^-2]

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Work (W) = Force × Displacement . . . . . (1)

Since, Force = Mass × acceleration = M × [L T^-2]

∴ The dimensional formula of Force = M¹ L¹ T^-2 . . . . (2)

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

Work = Force × Displacement

Or, W = [M¹ L¹ T^-2] × [M⁰ L¹ T⁰] = [M¹ L² T^-2].

Therefore, work is dimensionally represented as [M¹ L² T^-2].