Question

A block rests on a rough plane whose inclination $\theta$ to the horizontal can be varied. Which of the following graphs indicates how the frictional force $F$ between the block and the plane varies as $\theta$ is increased?

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

When the plane is horizontal there will be no frictional force acting as there will be no driving force. The maximum angle for the which the block remains stationary is called the angle of repose

Let $\alpha =$ angle of repose
For $\theta \le \alpha$, block is stationary and force of friction,
$f=mg\sin \theta$
or $f\propto \sin \theta$
i.e., it is sine graph
For $\theta \ge \alpha$ Block slides downwards
$\therefore f=\mu mg\cos \theta$
or $f\propto \cos \theta$
i.e, now it is cosine graph.

Hence option b will be the correct answer