Question

The velocity of centre of mass of a rolling disc is $v$. Considering sufficient friction to prevent any slipping, the magnitude of velocity at the highest point on the disc is

• A. $\sqrt{2}v$
• B. $v$
• C. $2v$
• D. $\frac{v}{\sqrt{2}}$

Answer 1

The correct option is C $2v$

Applying condition of pure rolling,
$v=r\omega ...\left(i\right)$
where $v=$ velocity of $\text{COM}$ of disc


Considering righwards as $+vex$ direction expressing the velocity at highest point $B$:
${\overrightarrow{v}}_B=v\hat{i}+r\omega \hat{i}=(v+r\omega )\hat{i}$
From Eq $\left(i\right)$
${\overrightarrow{v}}_B=(v+r\omega )\hat{i}=2v\hat{i}$
$|{\overrightarrow{v}}_B|=2v$