Which is true for rolling friction (${\\mu _r}$), static friction (${\\mu _s}$), and kinetic friction (${\\mu _k}$)?A. ${\\mu _s} > {\\mu _k} > {\\mu _r}$B. ${\\mu _s} < {\\mu _k} < {\\mu _r}$C. ${\\mu _s} < {\\mu _k} > {\\mu _r}$D. ${\\mu _s} > {\\mu _r} > {\\mu _k}$

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Question Answer

Class 11

Physics

Which is true for rolling fric...

Which is true for rolling friction ( $μ_{r}$ ), static friction ( $μ_{s}$ ), and kinetic friction ( $μ_{k}$ )?
A. $μ_{s} > μ_{k} > μ_{r}$
B. $μ_{s} < μ_{k} < μ_{r}$
C. $μ_{s} < μ_{k} > μ_{r}$
D. $μ_{s} > μ_{r} > μ_{k}$

Answer

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Hint: There are many types of frictions. The most common are rolling friction, static friction and kinetic or sliding friction.
Rolling friction (

μ_{r}

) as the name suggests is produced when an object on the ground.
Static friction (

μ_{s}

) is produced with two static objects or when two objects are not moving.
Kinetic friction (

μ_{k}

) acts between two moving bodies. Kinetic friction depends only on the surface on which it is moving.

Complete step by step solution:
The static friction is higher than kinetic friction. Static friction is required in holding an object at one place. So, much force is required for holding an object. Kinetic friction is a moving friction and as a result only a little amount of force is required. Hence, static friction is always greater than kinetic friction.
As a force or torque is applied to a stationary wheel, the rolling motion is held back by a weak, steady rotating friction force. Rolling friction is just the friction between a surface and an object when an object is rolled. Since, the force applied here is very weak, rolling friction is a much smaller friction as compared to static and kinetic friction. The reason for being a weak force is because wheels facilitate motion.
From the above discussion, we can say that among the three frictions static friction is the most powerful. Kinetic friction is somewhat more powerful than rolling friction.

Hence, option A is correct that is $μ_{s} > μ_{k} > μ_{r}$ .

Note: In this question we are asked to determine the relationship between rolling, kinetic and static friction.
We may get confused between rolling and kinetic friction, since both are moving friction. But kinetic friction is actually used for sliding of objects and rolling friction is produced when objects are rolled.