Question

A solid cylinder rolling down on an inclined plane as shown in figure. Which of the following options correctly depicts the motion of cylinder on the inclined plane?

• A. Cylinder is slipping forward
• B. Cylinder is slipping backward
• C. Cylinder is in pure rolling
• D. Friction is acting forward along plane

Answer 1

The correct option is A Cylinder is slipping forward

We know for pure rolling,
${\overrightarrow{v}}_{net}$ of point of contact $\left(P\right)$ of cylinder and plane is zero.


$\Rightarrow {\overrightarrow{v}}_{net}=0$
$\Rightarrow v-\omega R=0$
$\Rightarrow v=\omega R$ $[$ for pure rolling $]$
Given, $v=10\text{m/s}$..........(1)
$\omega =4\text{rad/s}$
Now, $\omega R=4\times 2=8\text{m/s}$..........(2)
Here, $v>\omega R$ $[$ from (1) and (2) $]$
As translational motion of the cylinder is more than rotational motion. Therefore, cylinder is slipping forward and friction force is acting upwards along the plane.