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If \[{\mu _S}\], ${\mu _K}$ and ${\mu _R}$ are the coefficients of limiting, kinetic and rolling frictions between two given surfaces. Arrange them in ascending order:
A) ${\mu _R} < {\mu _S} < {\mu _K}$
B) ${\mu _R} < {\mu _K} < {\mu _S}$
C) ${\mu _S} < {\mu _K} < {\mu _R}$
D) ${\mu _K} < {\mu _R} < {\mu _S}$

Last updated date: 20th Jun 2024
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Hint: In the given question, first of all, we need to know about the definitions of limiting, rolling and kinetic frictions. Then we need to find out the relation between these frictions and finally conclude with the solution.

Complete answer:
Limiting friction: It is the friction which is generated between the two static surfaces in contact with each other.
Kinetic friction: The force that acts between moving surfaces.
Rolling friction: It is the resistive force that slows down the motion of a rolling ball or wheel.
The limiting friction is the strongest friction followed by kinetic friction and rolling friction.
Clearly, limiting friction has the highest value and rolling friction has the lowest value.
So, we can write,
Rolling friction Now when we write it in formula wise, then we can write it as,
${\mu _S} < {\mu _K} < {\mu _R}$.

Hence, option (C) i.e. ${\mu _S} < {\mu _K} < {\mu _R}$ is the correct option.

Note: Friction is the force that opposes motion between any surfaces that are in contact. For example, when we try to push a book along the floor, friction makes this difficult. Friction always works in the direction opposite to the direction in which the object is moving, or trying to move. Basically, there are four types of friction, static, sliding, rolling and fluid friction. Static, sliding and rolling occurs between solid surfaces. Static friction is strongest, then sliding friction and then rolling friction which is the weakest one. Fluid friction occurs in fluid. So, if we compare we can write it as${\mu _S} < {\mu _K} < {\mu _R}$.