Dimensional representation of coefficient of friction isa)[ML2T-2]b)[MLT-2]c)[M0L0T0]d)[MLT-1]Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Mathematically, μ = F/L. Because both frictionand load are measured in units of force (such as pounds or newtons), the coefficient of friction is dimensionless.it can be [M^0L^0T^0]

Answer

C is correct option BECAUSE

coefficients of friction is dimensionless

i.e

[ M^0 L^0 T^0 ]

Answer

Understanding Coefficient of Friction
The coefficient of friction (μ) is a dimensionless quantity that describes the ratio of the force of friction between two bodies to the normal force acting on them.
Key Characteristics
- Dimensionless Nature: The coefficient of friction does not have any units, as it is a ratio. It compares two forces, the frictional force and the normal force, both measured in newtons (N).
- Forces Involved:
- Frictional Force (F_f): This is the force that opposes the relative motion of two surfaces in contact.
- Normal Force (N): This is the perpendicular force exerted by a surface on an object resting on it.
Dimensional Analysis
- When calculating the coefficient of friction, we use the formula:
μ = F_f / N
- Both F_f and N are measured in terms of force, which has the dimension of [MLT-2] (mass times acceleration).
Conclusion
- Since μ is the ratio of two forces, the dimensions cancel out:
[MLT-2] / [MLT-2] = [M0L0T0]
- Hence, the dimensional representation of the coefficient of friction is [M0L0T0], confirming that it is indeed a dimensionless quantity.
Correct Answer
- Therefore, the correct option is (C) [M0L0T0].

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