Question

A body remains at rest when it is pulled by a horizontal force of gradually increasing magnitude. For the given scenario the slope of the graph representing friction Vs applied force graph will be

• A. $1$
• B. $\mu$
• C. $0$
• D. $-1$

Answer 1

The correct option is A $1$

We know that untill the applied force exceeds the limiting value of static friction, friction will adjust its value according to the magnitude of force applied.

Thus the body will remain at rest if $F\le f_{\text{max}}$

The graph for applied force vs friction is shown in figure given below.


From the graph we can infer that the region $OA$ denotes the equilibrium of body in which the static friction acting on the body is of same magnitude as that of applied force and body remain in rest.

$\Rightarrow F=f....\left(i\right)$

Slope of $F\text{Vs}f$ graph,

$m=\tan \theta =\frac{f}{F}....\left(ii\right)$

From Eq.$\left(i\right)$ and $\left(ii\right)$ we conclude that,

$m=1$

Why this question ? $\underset{–}{\text{Concept involved:}}$The frictional force will increase linearly with applied force till its maximum value( represented by point $A$ in region $OA$), further increasing the applied force will lead to beginning of slipping and kinetic friction will act thereafter at a constant value $(f_k=\mu N)$. Region $BC$ in shown graph denotes kinetic friction$(f_k<f_{\text{limiting}})$