Question

A disc of radius $r$ is performing rotational and translational motion as shown in figure.



Choose the correct option.

• A. Velocity of point $A$ w.r.t point $B$ will always remain constant.
• B. Speed of point $A$ w.r.t point $B$ will always remain constant.
• C. Magnitude of relative velocity of point $A$ w.r.t point $B$ is $2\omega |{\overrightarrow{r}}_{AB}|\text{m/s}$.
• D. None of these.

Answer 1

The correct option is B Speed of point $A$ w.r.t point $B$ will always remain constant.

We know that,
${\overrightarrow{V}}_{AB}=\overrightarrow{\omega }\times {\overrightarrow{r}}_{AB}$
Now, ${\overrightarrow{r}}_{AB}$ will change as disc undergoes rotational and translational motion.
But, the magnitude of velocity
$|{\overrightarrow{V}}_{AB}|=|\overrightarrow{\omega }\times {\overrightarrow{r}}_{AB}|$ will remain constant throughout.
$\therefore$ option (b) is correct.