Question

The S.I unit of static coefficient of friction is:
A. N
B. Nm
C. \[\dfrac{{\text{N}}}{{\text{m}}}\]
D. It is unit less

Answer 1

Hint: The unit of any type of force is newton. To answer this question, you can recall the formula for static friction and rearrange the equation for coefficient of static friction.

Complete step by step solution:
We know that the static friction is the force provided by the surface and the body which is stationary of that surface. The static friction does not let the body to move from its stationary position.
We know the formula for static friction,
\[{f_s} = {\mu _s}N\]
Here, \[{\mu _s}\] is the coefficient of static friction and N is the normal force which is the force opposite to the direction of applied force on the body.
We can rearrange the above equation for \[{\mu _s}\] as follows,
\[{\mu _s} = \dfrac{{{f_s}}}{N}\]
Thus, we can see that the coefficient of static friction is the ratio of two forces. Static friction\[{f_s}\] has the unit newton and the normal force also has the unit newton.
Therefore, we can express the unit of coefficient of static friction as,
\[{\mu _s} = \dfrac{{\text{N}}}{{\text{N}}}\]
\[ \Rightarrow {\mu _s} = {{\text{N}}^0}\]

Therefore, we can say the coefficient of static friction is the unit less quantity.

So, the correct answer is “Option D”.

Additional Information:
The value of coefficient of static friction lies between 0 to 1. If the coefficient of static friction is 0, it means that there is not friction between the surface and body. Therefore, the frictional force will not oppose the applied force.

Note:
To answer these types of questions, the key is to recall the formula which can best suit to determine the unit of the given physical quantity. To do this, students should memorize the units of all the fundamental quantities like velocity, acceleration, force, pressure, etc. note that the dimensionless quantity may have unit but unit less quantity never have dimensions.