Question

The coefficient of limiting friction between the surfaces of contact is the ratio of the …… friction to the normal reaction.
A. Limiting
B. sliding
C. rolling
D. any of these

Answer 1

Hint: The force of the limiting friction is the product of the mass of the body/object and its acceleration. Whereas, the normal force is the product of the mass of the body/object and the gravitational constant. The coefficient of limiting friction is the ratio of acceleration to the gravitational constant.

Formula used:
\[\begin{align}
  & {{F}_{L}}=ma \\
 & N=mg \\
\end{align}\]
\[\mu =\dfrac{{{F}_{L}}}{N}\]

Complete answer:
The coefficient of limiting friction is given by,
\[\mu =\dfrac{{{F}_{L}}}{N}\]
Where \[{{F}_{L}}\]is the force of limiting friction and \[N\] is the normal force.
Thus, the coefficient of limiting friction between the surfaces of contact is the ratio of the limiting friction to the normal reaction.
\[{{F}_{L}}=ma\]
Where \[m\]is the mass of the object/body and \[a\] is the acceleration.
Thus, the force of limiting friction is the product of the mass of the body/object and its acceleration.
\[N=mg\]
Where \[m\]is the mass of the object/body and \[g\] is the gravitational constant.
Thus, the normal force is the product of the mass of the body/object and the gravitational constant.
Therefore, the coefficient of limiting friction between the surfaces of contact is the ratio of the limiting friction to the normal reaction.

Note:
The things to be on your figure tips for further information on solving these types of problems are:
There are different formulae to find the value of the coefficient of limiting friction. They are:
\[\mu =\dfrac{{{F}_{L}}}{N}\]and \[\mu =\tan \alpha \]
Use these formulae based on the given parameters.