Derive dimension formula of work and …

The dimensional formula of Work is given by,

M¹ L^-2 T^-2

Where,

• M = Mass
• L = Length
• T = Time

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].

The dimensional formula of force is given by,

M¹ L¹ T^-2

Where,

• M = Mass
• L = Length
• T = Time

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.