Dimensional Formula of Work

The dimensional formula of Work is given by,

M¹ L^-2 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].

⇒ Check Other Dimensional Formulas:

• Dimensions of Coefficient of Friction
• Dimensions of Charge
• Dimensions of Reynolds Number
• Dimensions of Magnetic Flux
• Dimensions of Gravitational Potential Energy

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