Question

A wheel of radius $r$ rolls without slipping with a speed $v$ on a horizontal road. When it is at a point A on the road, a small blob of mud separates from the wheel at its highest point and lands at point B on the road.

• A. $AB=v\sqrt{\frac{r}{g}}$
• B. $AB=2v\sqrt{\frac{r}{g}}$
• C. $AB=4v\sqrt{\frac{r}{g}}$
• D. If $v>\sqrt{4rg}$, the blob of mud will land on the wheel and not on the road.

Answer 1

Answer: (C)

$AB=4v\sqrt{\frac{r}{g}}$

The blob of mud would have a velocity of 2v and an initial height of 2r. Thus time of travel t is given using $s=ut+\frac{1}{2}a{t}^2$
or
$2r=\frac{1}{2}g{t}^2$
or
$t=2\sqrt{\frac{r}{g}}$
Thus distance AB is given as $2vt=4v\sqrt{\frac{r}{g}}$