Question

what are dimension of friction ? full derivation

Answer 1

Dimensional Formula of Coefficient of Friction

The dimensional formula of coefficient of friction is given by,

[M⁰L⁰T⁰]

Where,

• M=Mass
• L=Length
• T=Time

Derivation

Coefficient of friction (μ) = Frictional Force × [Normal Force]-¹ . . . . (1)

Since, Force (F) = Mass × acceleration = Mass × velocity × [Time]-¹

And, velocity = Displacement × [Time]-¹

∴ The dimensions of Force = [M] × [LT-¹] × [T]-¹ = [M¹ L¹ T-²] . . . . (2)

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

Coefficient of friction (μ) = Frictional Force × [Normal Force]-¹

Or, μ = [M¹ L¹ T-²] × [M¹ L¹ T-²]-¹ = [M⁰ L⁰ T⁰].

Therefore, the coefficient of friction is dimensionally represented as [M⁰ L⁰ T⁰].

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