Question

A wheel of radius 'r' rolls without slipping with a speed 'v' on a horizontal road. When it is at point 'A' on the road, a small lump of mud separates from the wheel at its highest point 'C' on the road. The distance AC will be:

• A. $v\sqrt{\frac{r}{g}}$
• B. $2v\sqrt{\frac{r}{g}}$
• C. $4v\sqrt{\frac{r}{g}}$
• D. $v\sqrt{\frac{3r}{g}}$

Answer 1

The correct option is C $4v\sqrt{\frac{r}{g}}$

At the point of leaving the wheel at D, bob's velocity is $2v$ along

Time of flight $2r=\frac{1}{2}g{t}^2\Rightarrow t=2\sqrt{\frac{r}{g}}$

Distance covered horizontally $=2v\times 2\sqrt{\frac{r}{g}}$

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