Question

The SI unit of static coefficient of friction is

A.)$N$
B.)$Nm$
C.)$\dfrac{N}{m}$
D.)It is unit less.

Answer 1

Hint- As we know the maximum ratio of force applied to normal force with no motion is frictional force which opposes the motion. The force applied on a body is at rest upto a certain point till the body is able to resist the force applied. The maximum of this resistive force offered by the body against the applied force to continue its state of motion is known as coefficient of friction. We will derive the unit of coefficient of friction using its definition and formula.

Complete step-by-step answer:
The coefficient of friction depend upon following factors

Heaviness of the material, rough surface, the roughness of the material is measured using the parameter called coefficient of static friction.

The coefficient of static friction is mathematically given by

$
  F = {\mu _s}N \\
  {\mu _s} = \dfrac{F}{N} \\
 $

Where N is the normal force which is perpendicular to the direction of the applied force and F is the frictional force.

As we know the units of force are newton and normal is also a force, hence its unit is also newton. The two forces units will cancel each other. Therefore, the coefficient of friction has no unit.

${\mu _s} = \dfrac{{newton}}{{newton}} = newto{n^{^0}}$

It is a unit less and dimensionless quantity.

Hence, the correct option is D.

Note- To solve these types of questions, the first thing you need to remember is the formula of the quantity whose unit has been asked. For determining the dimension, substitute the units of other quantities and cancel out the like terms. After cancelling the like terms, we will get our unit of the quantity which we have been asked. Similarly dimension can be calculated.