Question

In a situation, the contact force by a rough horizontal surface on a body placed on it has constant magnitude. If the angle between this force and the vertical is decreased, the frictional force between the surface and the body will

• A. $\text{increase}$
• B. $\text{decrease}$
• C. $\text{remain same}$
• D. $\text{may increase or decrease}$

Answer 1

The correct option is B $\text{decrease}$

Let us draw the condition given in the question

For the constant magnitude of the contact force we can write
$N=mg-R\cos \theta$
and we know that friction force, $f=\mu N\Rightarrow f=\mu (mg-R\cos \theta )$
Thus, if $\theta$, decreases, $R$ will shift towards normal reaction force and $\cos \theta$ value will increase. This ultimately results in the decrement of frictional force.
Hence, frictional force will decrease in this case.