Question

$A$ block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and tan $\theta >\mu.$ The block is held stationary by applying a force $P$ parallel to the plane. The direction of force pointing up the plane is taken to be positive. As $P$ is varied from $P_{1}=mg$ $\left(sin\,\theta-\mu\,cos\,\theta\right)$ to $P_{2}=mg$ $\left(sin\theta+\mu cos\theta\right)$, the frictional force $f$ versus $P$ graph will look like

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

Answer 2

From $FBD$ of block, $N=mg \,cos \theta$
$p+f=mg \,sin\, \theta$ or $f=mg\,sin \,\theta-p$

As $P$ varies from $mg$ $\left(sin\,\theta-\mu cos\,\theta\right)$ to $mg$ $\left(sin\,\theta+\mu cos\,\theta\right)$,
$f$ varies from +$\mu \,mg\,cos\,\theta$ to $-\mu\, mg \,cos \,\theta$.
This value of friction is always less than or equal to $\mu N$ in magnitude.