# Dimensions of Work

## 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 = [MLT-2] × [MLT0] = [M1 LT-2].

Therefore, work is dimensionally represented as [M1 LT-2].