A) \[{{\mu }_{s}}>{{\mu }_{k}}>{{\mu }_{r}}\]
B) \[{{\mu }_{s}}<{{\mu }_{k}}<{{\mu }_{r}}\]
C) \[{{\mu }_{s}}<{{\mu }_{k}}>{{\mu }_{r}}\]
D) \[{{\mu }_{s}}<{{\mu }_{r}}>{{\mu }_{k}}\]
Correct Answer: A
Solution :
Key Idea: Lesser force is required to maintain the motion of a body than force required to start the body from rest. The limiting (maximum) static frictional force depends upon the nature of the surfaces in contact. It does not depend upon the size or area of the surfaces. For the given surfaces, the limiting frictional force\[{{f}_{s}}\]is directly proportional to normal reaction R\[{{f}_{s}}={{\mu }_{s}}R\] Once the body starts motion, the frictional force acting between the surfaces decreases so a smaller force F is required to maintain uniform motion. The force acting between the surfaces in relative motion is called the dynamical frictional force\[{{f}_{k}}\]which is less than limiting force of static friction\[{{f}_{s}}\]. \[\therefore \] \[{{\mu }_{k}}<{{\mu }_{s}}\] Once the body starts sliding it continues to slide at a constant speed at\[{{\mu }_{r}}\]being coefficient of rolling friction. Hence, we have \[{{\mu }_{s}}>{{\mu }_{k}}<{{\mu }_{r}}\]
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